Trigonometry Sheet-1 PDF SSC CHSL TIER-I 2022

41 1. If cosec = and  is an acute angle, then the value of 5 tan will be: 9 41 ;fn cosec = gS vkSj  U;wu dks.k gS] rks 5tan dk eku Kkr djsAa 9 11 (a) 8 13...

41 1. If cosec = and  is an acute angle, then the value of 5 tan will be: 9 41 ;fn cosec = gS vkSj  U;wu dks.k gS] rks 5tan dk eku Kkr djsAa 9 11 (a) 8 13 (b) 4 7 (c) 8 9 (d) 8 2. If cos = 9/13, then what is the value of cosec ? 𝟏𝟑 (a) √𝟐𝟐 𝟏𝟑√𝟐𝟐 (b) 𝟒𝟒 𝟐√𝟐𝟐 (c) 𝟏𝟑 √𝟐𝟐 (d) SSC CHSL TIER – I 2022 𝟏𝟑 3. If 4cot A = 5, then what is the value of 6 sec A tan A? ;fn 4cot A = 5, rks 6 sec A tan A dk eku D;k gS\ 𝟐𝟎√𝟒𝟏 (a) 𝟐𝟏 𝟐𝟓√𝟒𝟏 (b) 𝟐𝟒 𝟐𝟒√𝟒𝟏 (c) 𝟐𝟓 (d) 3/2 SSC CHSL TIER – I 2022 𝟑𝒔𝒊𝒏²𝜽+𝒄𝒐𝒔𝜽 4. If sin  = √𝟑 cos  then what is the value of ? 𝟐𝒄𝒐𝒔𝜽+𝟓 𝟑𝒔𝒊𝒏²𝜽+𝒄𝒐𝒔𝜽 ;fn sin  = √𝟑 cos  rks dk eku D;k gS\ 𝟐𝒄𝒐𝒔𝜽+𝟓 (a) 19/25 (b) 18/5 (c) 11/24 (d) 3/2 SSC CHSL TIER – I 2022 Telegram channel By Gagan Pratap Sir- https://t.me/mathsbygaganpratap Join Full Batch Download Careerwill App- https://bit.ly/CareerwillApp 5. Find the value of 𝒄𝒐𝒕𝟏𝟏𝟏𝟎 √𝐬𝐞𝐜 𝟐 𝟏𝟏𝟏𝟎 − 𝟏 𝒄𝒐𝒕𝟏𝟏𝟏𝟎 √𝐬𝐞𝐜 𝟐 𝟏𝟏𝟏𝟎 − 𝟏 dk eku Kkr djsaA (A) cot21110 (B) 1 (C) tan2210 (D) – 1  3  6. If sec  90 −  = 2 , 0° <  < 90°, then the value of 2 sin + 4cos 2 will be :  2   3  ;fn sec  90 −  = 2 , 0° <  < 90° gS] rks 2 sin + 4cos 2 dk eku Kkr djsaA  2  (a) 4 (b) 2 (c) 3 (d) 6 7. If tan(x+y) = 1 and cos(x–y) = √𝟑/𝟐, then what is the value of x and y? ;fn tan(x+y) = 1 and cos(x–y) = √𝟑/𝟐, rks x vkSj y dk eku D;k gS\ (a) x = 3, y = 4.5 (b) x = 37.5, y = 7.5 (c) X = 7.5, y = 37.5 (d) x = 4.5, y =3 SSC CHSL TIER – I 2022 8. If cot = 𝟏𝟓 ,  is an acute angle, then find the value of (1-cosθ )( 2+2cosθ ). 𝟖 ( 2-2sinθ )(1+sinθ ) ;fn cot = 𝟏𝟓 gS]  U;wu dks.k gS] rks (1-cosθ )( 2+2cosθ ) dk eku Kkr djsaA 𝟖 ( 2-2sinθ )(1+sinθ ) 𝟏𝟔 (a) 𝟏𝟓 𝟔𝟒 (b) 𝟐𝟐𝟓 𝟐𝟐𝟓 (c) 𝟔𝟒 𝟖 (d) 𝟏𝟓 9. If 5cosθ=4sinθ,0o  θ  90o , then what will be the value of secθ. ;fn 5cosθ=4sinθ,0o  θ  90o gS] rks secθ dk eku Kkr djsaA 41 (a) 5 Telegram channel By Gagan Pratap Sir- https://t.me/mathsbygaganpratap Join Full Batch Download Careerwill App- https://bit.ly/CareerwillApp  3 (b) 5 41 (c) 16 41 (d) 4 10. If cosec A = 10, then what is the value of 20 sin A + 9 11 sec A? ;fn cosec A = 10 gS] rks 20 sin A + 9 11 sec A dk eku Kkr djsAa Given that A is an acute angle. fn;k x;k gS fd] A U;wu dks.k gSA (a) 23 (b) 34 (c) 32 (d) 30 𝟕 𝟑 11. If cos 𝜽 = 𝟑√𝟔 and 𝜽 is an acute angle , then the value of 27 sin2𝜽 - 𝟐 is: 𝟕 𝟑 ;fn cos 𝜽 = 𝟑√𝟔 gS vkSj 𝜽 U;w.k dks.k gS] rks 27 sin2𝜽 - 𝟐dk eku Kkr djsAa (a) 12 (b) 15 (c) 1 (d) 9 12. If sin + cos = √𝟐 , then find the value of cosec + cot ;fn sin + cos = √𝟐 gS] rks cosec + cot dk eku Kkr dhft,A (a) √𝟐 − 𝟏 (b) √𝟐 + 𝟓 (c) √𝟑 − 𝟏 (d) √𝟐 + 𝟏 SSC CHSL TIER – I 2022 13. If cot = 2 + 1 , then cosec sec = ? ;fn cot = 2 + 1gS] rks cosec sec dk eku Kkr djsaA 2 (a) 2 Telegram channel By Gagan Pratap Sir- https://t.me/mathsbygaganpratap Join Full Batch Download Careerwill App- https://bit.ly/CareerwillApp  (b) 4 2 2 (c) 4 (d) 2 2 𝒂 14. 𝒄𝒐𝒔 𝟏 𝟗° = 𝒃 then 𝒄𝒐𝒔 𝒆 𝒄𝟏𝟗° − 𝒄𝒐𝒔 𝟕 𝟏° =? 𝒃𝟐 𝒂𝟐 𝒂𝟐 𝒃𝟐 𝒂𝒃 a) b) c) d) 𝒂√𝒂𝟐 −𝒃𝟐 𝒃√𝒃𝟐 −𝒂𝟐 √𝒂𝟐 −𝒃𝟐 √𝒃𝟐 −𝒂𝟐 15. In ∆ABC, ∠C=90° and AB=c, BC=a, CA=b, then find the value of (cosecB-cosA)? 𝒄𝟐 𝒃𝟐 𝒂𝟐 𝒃𝒄 a)𝒂𝒃 b) 𝒄𝒂 c) 𝒃𝒄 d) 𝒂𝟐 15.1 In ABC, AB = 20 cm, BC = 21 cm and AC = 29 cm. What is the value of cot C + cosec C – 2 tanA? ABC eas] AB = 20 cm, BC = 21 cm vkSj AC = 29 cm gSA cot C + cosec C – 2 tanA dk eku Kkr djsAa 𝟗 (a) 𝟐𝟎 𝟕 (b) 𝟐𝟎 𝟐 (c) 𝟓 𝟑 (d) 𝟓 𝒄𝒐𝒔𝒆𝒄𝟐 𝟐𝜽+𝒄𝒐𝒕𝟐 𝟐𝜽 16. If 𝟑𝒕𝒂𝒏𝜽 = 𝟐√𝟑 𝒔𝒊𝒏𝜽, 8. 0° 0, then the value of will be: a+b cosθ-1 2 ab cosθ+1 ;fn sin = gS] a > b > 0 gS] rks dk eku Kkr djsaA a+b cosθ-1 b (a) - a a (b) − b 𝒂 (c) 𝒃 𝒃 (d) 𝒂 Telegram channel By Gagan Pratap Sir- https://t.me/mathsbygaganpratap Join Full Batch Download Careerwill App- https://bit.ly/CareerwillApp   2A+B   2A-B  3 2A+B 2A+B 22. If sin   =cos  = ,0°, < 90 and 0° < < 90° then find the value of sin[3(A–  2   2  2 2 2 B)].  2A+B   2A-B  3 2A+B 2A+B ;fn sin   =cos  = ,0°, < 90 vkSj 0° < < 90° gS] rks sin[3(A–B)] dk eku Kkr djsaA  2   2  2 2 2 (a) 1 1 (b) 2 𝟏 (c) 𝟐 3 (d) 2 2 23. If (cos + sin): (cos - sin) = (√𝟑 + 1) : (√𝟑 - 1), 0 <  < 900, then what is the value of sec? ;fn (cos + sin): (cos - sin) = (√𝟑 + 1) : (√𝟑 - 1), 0 <  < 900 gS] rks sec dk eku D;k gksxk\ 𝟐√𝟑 (a) (b) 1 (c) √𝟐 (d) 2 𝟑 𝟏 𝟏 𝟏 24. If Sinθ=√𝟔 √𝟔 √𝟔 − − − − − − − − − − − − − ∞ Then, tanθ+cotθ=? 𝟑𝟔 𝟑𝟔 √𝟑𝟓 𝟑𝟓 a) b)𝟑𝟓 c) 𝟑𝟔 d)√𝟑𝟔 √𝟑𝟓 𝟖 𝟏𝟓 25. Sin𝛉 = , tan𝛂 = , then find cos(𝛉+𝛂) = ? 𝟏𝟕 𝟖 𝟐𝟑 𝟏𝟓 a)0 b)1 c)𝟏𝟕 d)𝟏𝟕 26. If cos  – sin = 3 cos(90°–), 0° <  < 90° then find the value of tan – cot. ;fn cos  – sin = 3 cos(90°–), 0° <  < 90° gS] rks tan – cot dk eku Kkr djsAa 3+ 2 3 (a) ( 1+ 3 ) 3+ 2 3 (b) − ( 1+ 3 ) 3+ 2 3 (c) − ( 1− 3 ) Telegram channel By Gagan Pratap Sir- https://t.me/mathsbygaganpratap Join Full Batch Download Careerwill App- https://bit.ly/CareerwillApp  3− 2 3 (d) ( 1+ 3 ) sin 4 ( x − 5) + cos 4 ( x − 5) 27. If 4 sin²(2x–10)° = 3, 0  (2x–10)  90, then find the value of. 1 − 2sin 2 (3x − 15) cos 2 (3 x − 15) sin 4 ( x − 5) + cos 4 ( x − 5) ;fn 4 sin²(2x–10)° = 3, 0  (2x–10)  90gS] rks dk eku Kkr djsAa 1 − 2sin 2 (3x − 15) cos 2 (3 x − 15) (a) 1 𝟓 (b) 𝟖 𝟓 (c) −𝟖 (d) –1 𝟏𝟐 𝒔𝒊𝒏𝜽(𝟏−𝒕𝒂𝒏𝜽) 28. If cos𝜽 = 𝟏𝟑 , 𝒕𝒉𝒆𝒏 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 is: 𝒕𝒂𝒏𝜽(𝟏+𝒄𝒐𝒔𝒆𝒄𝜽) 𝟏𝟐 𝒔𝒊𝒏𝜽(𝟏−𝒕𝒂𝒏𝜽) यदि cos𝜽 = 𝟏𝟑 है तो 𝒕𝒂𝒏𝜽(𝟏+𝒄𝒐𝒔𝒆𝒄𝜽) का मान क्या होगा? 𝟐𝟓 𝟑𝟓 𝟑𝟓 𝟐𝟓 (a) 𝟕𝟖 (b) 𝟐𝟑𝟒 (c) 𝟏𝟎𝟖 (d) 𝟏𝟓𝟔 29. If 6 sec  = 10, then find the value of (5 cosec  – 3 cot )/(4 cos + 3 sin). ;fn 6 sec  = 10 gS] rks (5 cosec  – 3 cot )/(4 cos + 3 sin) dk eku Kkr dhft,A (a) 2/3 (b) 3/2 (c) 5/6 (d) 6/5 SSC CHSL TIER – I 2022 cosecθ+cotθ 4sin 2 θ+5 30. If = 7, then the value of is: cosecθ-cotθ 4sin 2 θ-1 cosecθ+cotθ 4sin 2 θ+5 ;fn = 7 gS] rks dk eku Kkr djsAa cosecθ-cotθ 4sin 2 θ-1 (a) 15 (b) 3 (c) 9 (d) 12 𝒔𝒆𝒄𝜽−𝒕𝒂𝒏𝜽 𝟏 𝒄𝒐𝒔𝒆𝒄𝜽+𝒄𝒐𝒕𝟐 𝜽 31. If 𝒔𝒆𝒄𝜽+𝒕𝒂𝒏𝜽 = 𝟕 ,θ lies in first quadrant, then the value of 𝒄𝒐𝒔𝒆𝒄𝜽−𝒄𝒐𝒕𝟐 𝜽 is 𝒔𝒆𝒄𝜽−𝒕𝒂𝒏𝜽 𝟏 𝒄𝒐𝒔𝒆𝒄𝜽+𝒄𝒐𝒕𝟐 𝜽 यदि 𝒔𝒆𝒄𝜽+𝒕𝒂𝒏𝜽 = 𝟕, θ प्रथम चतुथाांश में दथथत है, तो 𝒄𝒐𝒔𝒆𝒄𝜽−𝒄𝒐𝒕𝟐 𝜽 =? Telegram channel By Gagan Pratap Sir- https://t.me/mathsbygaganpratap Join Full Batch Download Careerwill App- https://bit.ly/CareerwillApp  𝟏𝟗 𝟐𝟐 𝟑𝟕 𝟑𝟕 (a) (b) (c) 𝟏𝟐 (d) 𝟏𝟗 𝟓 𝟑 𝟓𝒔𝒊𝒏𝜽−𝟐𝒄𝒐𝒔𝜽 32. If 5sin – 4cos = 0, 0° <  < 90°, then the value of 𝟓𝒔𝒊𝒏𝜽+𝟑𝒄𝒐𝒔𝜽 is: 𝟓𝒔𝒊𝒏𝜽−𝟐𝒄𝒐𝒔𝜽 यदि 5sin – 4cos = 0, 0° <  < 90° है, तो का मान है: 𝟓𝒔𝒊𝒏𝜽+𝟑𝒄𝒐𝒔𝜽 𝟑 𝟐 𝟓 𝟑 a) 𝟕 b) 𝟕 c) 𝟖 d) 𝟖 𝟓 𝟏𝟖𝒔𝒊𝒏𝜽−𝟕𝒄𝒐𝒔𝜽 33. If 𝒕𝒂𝒏𝜽 = 𝟗, then 𝟗𝒔𝒊𝒏𝜽+𝟏𝟏𝒄𝒐𝒔𝜽 is eqaul to: 𝟓 𝟏𝟖𝒔𝒊𝒏𝜽−𝟕𝒄𝒐𝒔𝜽 ;fn 𝒕𝒂𝒏𝜽 = 𝟗, gks rks 𝟗𝒔𝒊𝒏𝜽+𝟏𝟏𝒄𝒐𝒔𝜽 dk eku gksxk\ 𝟓 𝟑 𝟐 𝟒 a) 𝟏𝟒 b)𝟏𝟔 c) 𝟓 d) 𝟏𝟏 6 sin θ – 3 cos θ 34. If 5 cot θ = 3, find the value of 7 sin θ + 3 cos θ यदि 5 cotθ = 3 है , तो 𝟕𝒔𝒊𝒏𝜽+𝟑𝒄𝒐𝒔𝜽 का मान ज्ञात कीजिए। 𝟔𝒔𝒊𝒏𝜽−𝟑𝒄𝒐𝒔𝜽 𝟐𝟎 𝟒𝟒 𝟏𝟏 𝟐𝟏 (A) 𝟒𝟏 (B) 𝟐𝟏 (C) 𝟒𝟎 (D) 𝟒𝟒 𝒄𝒐𝒔𝒆𝒄𝟐 𝜽+𝒔𝒆𝒄𝟐 𝜽 35. If 𝒄𝒐𝒕𝜽 = √𝟔, then the value of 𝒄𝒐𝒔𝒆𝒄𝟐𝜽−𝒔𝒆𝒄𝟐 𝜽is: 𝒄𝒐𝒔𝒆𝒄𝟐 𝜽+𝒔𝒆𝒄𝟐 𝜽 यदि 𝒄𝒐𝒕𝜽 = √𝟔 है तो 𝒄𝒐𝒔𝒆𝒄𝟐 𝜽−𝒔𝒆𝒄𝟐 𝜽 का मान : 𝟒𝟗 𝟒𝟑 𝟕 𝟒𝟖 a)𝟑𝟔 b)𝟑𝟔 c)𝟓 d)𝟑𝟓 𝟐 𝟑𝒄𝒐𝒔𝒆𝒄𝟐 𝜽 + 𝟐𝒔𝒆𝒄𝟐 𝜽 36. If tanθ = , then the value of will be: √𝟏𝟑 𝟓𝒄𝒐𝒔𝒆𝒄𝟐 𝜽 − 𝟒𝒔𝒆𝒄𝟐 𝜽 𝟐 𝟑𝒄𝒐𝒔𝒆𝒄𝟐 𝜽 + 𝟐𝒔𝒆𝒄𝟐 𝜽 यदि tanθ = , तो का मान होगा: √𝟏𝟑 𝟓𝒄𝒐𝒔𝒆𝒄𝟐 𝜽 − 𝟒𝒔𝒆𝒄𝟐 𝜽 𝟒𝟏 𝟒𝟕 (a) (b) 𝟒𝟓 𝟒𝟗 𝟒𝟔 𝟓 (c) (d) 𝟓𝟑 𝟕 √𝟏𝟎 𝒄𝒐𝒔𝒆𝒄𝟐 𝑨+𝐭𝐚𝐧𝟐 𝑨 37. If 𝒄𝒐𝒔𝑨 = , then the value of is: √𝟏𝟓 𝐬𝐢𝐧𝟐 𝑨+𝐜𝐨𝐭 𝟐 𝑨 𝒄𝒐𝒔𝒆𝒄𝟐 𝐀+𝐓𝐚𝐧𝟐 𝐀 अगर 𝒄𝒐𝒔𝐀 = है , तो का मान ज्ञात कीजिए। √𝟏𝟎 √𝟏𝟓 𝐬𝐢𝐧𝟐 𝐀+𝑪𝒐𝒕𝟐 𝐀 𝟗 𝟒 𝟑 𝟐 (a) (b) (c) (d) 𝟒 𝟗 𝟐 𝟑 𝒔𝒆𝒄𝜽−𝒕𝒂𝒏𝜽 𝟑 𝒄𝒐𝒔𝒆𝒄𝜽+𝒄𝒐𝒕𝜽 38. If 𝒔𝒆𝒄𝜽+𝒕𝒂𝒏𝜽 = 𝟓, then the value of 𝒄𝒐𝒔𝒆𝒄𝜽−𝒄𝒐𝒕𝜽 𝒊𝒔: − यदि 𝒔𝒆𝒄𝜽+ 𝒕𝒂𝒏𝜽 = 𝟓 है, तो का मान बताइए। 𝒔𝒆𝒄𝜽 − 𝒕𝒂𝒏𝜽 𝟑 𝒄𝒐𝒔𝒆𝒄𝜽+𝒄𝒐𝒕𝜽 𝒄𝒐𝒔𝒆𝒄𝜽 −𝒄𝒐𝒕𝜽 a) 31+8√15 b) 33+4√15 c) 27+√15 d) 24+√15 39. If x=asinθ-bcosθ, y=acosθ+bsinθ, then which of the following is true? 𝒙𝟐 𝒂𝟐 𝒙𝟐 𝒚𝟐 a)𝒚𝟐 +𝒃𝟐 = 1 b)x2+y2=a2- b2 c)x2+y2=a2+b2 d) +𝒃𝟐 = 1 𝒂𝟐 40. If xcos A – y sinA = 1 and xsinA+ ycosA = 4, then the value of 17𝒙𝟐 + 𝟏𝟕𝒚𝟐 is: यदि xcos A – y sinA = 1 and xsinA+ ycosA = 4 है तो 17𝒙𝟐 + 𝟏𝟕𝒚𝟐 का मान क्या है ? a) 7 b) 49 c) 0 d) 289 Telegram channel By Gagan Pratap Sir- https://t.me/mathsbygaganpratap Join Full Batch Download Careerwill App- https://bit.ly/CareerwillApp  𝒙−𝒂 𝟐 𝒚−𝒃 𝟐 𝒛 𝟐 41. 𝒙 = 𝒂 + 𝒂𝒔𝒊𝒏𝜶. 𝒄𝒐𝒔𝜷, 𝒚 = 𝒃(𝟏 + 𝒔𝒊𝒏𝜶. 𝒔𝒊𝒏𝜷), 𝒛 = 𝒄. 𝒄𝒐𝒔𝜶, then ( 𝒂 ) + ( ) + (𝒄) =? 𝒃 a)3 b)1 c)-1 d)0 42. (𝟏 − 𝒔𝒊𝒏𝑨. 𝒄𝒐𝒔𝑨)(𝒔𝒊𝒏𝑨 + 𝒄𝒐𝒔𝑨) =? a) 𝒔𝒊𝒏𝟐 𝑨 − 𝒄𝒐𝒔𝟐 𝑨 b) 𝒔𝒊𝒏𝟑 𝑨 + 𝒄𝒐𝒔𝟑 𝑨 c) 𝒄𝒐𝒔𝟐 𝑨 − 𝒔𝒊𝒏𝟐 𝑨 d) 0 43. If 𝒔𝒊𝒏 𝜽 , 𝒄𝒐𝒔 𝜽 and 𝒕𝒂𝒏 𝜽 are in G.P., then find 𝒄𝒐𝒕𝟔 𝜽 − 𝒄𝒐𝒕𝟐 𝜽 =? a)-1 b)1 c)0 d)2 44. In a triangle ABC, right angled at B,AB= 7 and(AC-BC)= 1cm. The value of (secA+cotC) is: ∆ABC esa B ij ledks.k gS] AB=7cm vkSj (AC-BC)=1cm gSA (secA+cotC) dk eku gS: 𝟒 𝟑 𝟏𝟕𝟓 a) 𝟑 b) 𝟒 c) d) 7 𝟐𝟒 45. In a right ∆ABC, ∠B=90°, AC-BC=2, AB=4√2, Then secA+cotC? a) 2√2 b) 4√2 c) 3√2 d) 5/√2 46. If secx + cosx = 3, then tan2x – sin2x =? a) 5 b) 13 c) 9 d) 4 𝒄𝒐𝒕𝑨+𝒕𝒂𝒏𝑩 47. What is the simplified value of 𝒄𝒐𝒕𝑩+𝒕𝒂𝒏𝑨 =? a) tanBcotA b) tanAcotB c) tanAtanB d) cotAcotB 48. If 00 ≤  ≤ 900, and sec107 + cos107 = 2, then, (sec + cos) is equal to: ;fn 00 ≤  ≤ 900 vkSj sec107 + cos107 = 2 gS] rks (sec + cos) dk eku Kkr dhft,A (a) 2-107 (b) 2 (c) ½ (d) 1 √𝟑𝒔𝒆𝒄𝜽+𝒕𝒂𝒏𝜽 49. If 𝟕𝒔𝒊𝒏𝟐 𝜽 + 𝟒𝒄𝒐𝒔𝟐 𝜽 = 𝟓 and 𝜽 lies in the first quadrant, then what is the value of ? √𝟐𝒄𝒐𝒕𝜽−√𝟑𝒄𝒐𝒔𝜽 यदि 𝟕𝒔𝒊𝒏𝟐 𝜽 + 𝟒𝒄𝒐𝒔𝟐 𝜽 = 𝟓 और 𝜽 पहले चतुर्ाांश में जथर्त है , तो का मान क्या है ? √𝟑𝒔𝒆𝒄𝜽+𝒕𝒂𝒏𝜽 √𝟐𝒄𝒐𝒕𝜽−√𝟑𝒄𝒐𝒔𝜽 (a) 𝟐(𝟏 + √𝟐) (b)𝟑√𝟐 (c) 𝟐(√𝟐 − 𝟏) (d) 𝟒√𝟐 𝒔𝒊𝒏²𝜽 𝟐𝟒𝒔𝒊𝒏²𝜽−𝟏𝟓𝒔𝒆𝒄²𝜽 50. If 𝒕𝒂𝒏²𝜽–𝒔𝒊𝒏²𝜽 = 5,  is an acute angle, then the value of is: 𝟔𝒄𝒐𝒔𝒆𝒄²𝜽−𝟕𝒄𝒐𝒕²𝜽 𝒔𝒊𝒏²𝜽 𝟐𝟒𝒔𝒊𝒏²𝜽−𝟏𝟓𝒔𝒆𝒄²𝜽 ;fn 𝒕𝒂𝒏²𝜽–𝒔𝒊𝒏²𝜽 = 5 gS]  U;wu dks.k gS] rks dk eku Kkr djsaA 𝟔𝒄𝒐𝒔𝒆𝒄²𝜽−𝟕𝒄𝒐𝒕²𝜽 (a) 2 (b) –14 (c) 14 (d) –2 cos 2θ 51. If = 3, 0° <  < 90°, then the value of (tan  + cosec) is: cot 2θ+sin 2θ-1 cos 2θ ;fn = 3 gS] 0° <  < 90° gS] rks (tan  + cosec) dkeku Kkr djsAa cot 2θ+sin 2θ-1 Telegram channel By Gagan Pratap Sir- https://t.me/mathsbygaganpratap Join Full Batch Download Careerwill App- https://bit.ly/CareerwillApp  (a) 2 3 5 3 (b) 3 (c) 3 3 4 3 (d) 3 52. If 3cos = sin2     then what is the value of (tan2+ sec2− cosec2) ;fn 3cos = sin2      gS] rks (tan2+ sec2− cosec2) dk eku Kkr djsAa 𝟏𝟕 (a) 𝟑 𝟕 (b) −𝟑 𝟏𝟕 (c) − 𝟑 𝟕 (d) 𝟑 53. If 𝟑 𝒔𝒆𝒄 𝜽 + 𝟒𝒄𝒐𝒔 𝜽 – 𝟒√𝟑 = 𝟎where  is an acute angle than the value of  is: ;fn 𝟑 𝒔𝒆𝒄 𝜽 + 𝟒 𝒄𝒐𝒔 𝜽 – 𝟒√𝟑 = 𝟎gS]  U;wu dks.k gS] rks  dk eku Kkr djsAa (a)20° (b)30° (c)60° (d)45° 54. If 5sin² = 3(1 + cos), 0° <  < 90°, then the value of cosec + cot is: ;fn 5sin² = 3(1 + cos), 0° <  < 90° gS] rks cosec + cot dk eku Kkr djsaA 7 (a) 3 5 (b) 21 4 (c) 21 3 (d) 7 55. Solve the following equation/fuEu lehdj.k dk eku Kkr djsaA   2 3 sin²  + cos – 3 = 0 where  is an acute angle /tgk¡  U;wu dks.k gSA (a) 30° (b) 45° Telegram channel By Gagan Pratap Sir- https://t.me/mathsbygaganpratap Join Full Batch Download Careerwill App- https://bit.ly/CareerwillApp  (c) 60° (d) 15° 𝒔𝒆𝒄𝜽+𝒄𝒐𝒕𝜽 56. If 5 𝒔𝒊𝒏𝟐 𝜽 + 𝟏𝟒𝒄𝒐𝒔𝜽 = 𝟏𝟑, 𝟎° < 𝜽 < 𝟗𝟎°, then what is the value of ? 𝒄𝒐𝒔𝒆𝒄𝜽+𝒕𝒂𝒏𝜽 यदि 5sin2 𝜽 + 14cos 𝜽 = 13, 0o < 𝜽 < 90o है , तो का मान क्या होगा? sec𝜽 + cot𝜽 cosec𝜽 + tan𝜽 𝟗 𝟑𝟏 𝟐𝟏 𝟑𝟐 a) 𝟖 b) 𝟐𝟗 c) 𝟐𝟖 d) 𝟐𝟕 𝟐 57. If 2 sin θ + 15 𝒄𝒐𝒔 𝜽 = 𝟕, 𝟎° < 𝜽 < 𝟗𝟎°, 𝒕𝒉𝒆𝒏 𝒕𝒂𝒏𝜽 + 𝒄𝒐𝒔𝜽 + 𝒔𝒆𝒄𝜽 =? यदि 2sin𝜽 + 15 cos2 𝜽 = 7, 𝟎o < 𝜽 < 90o है, तो tan 𝜽 + cos 𝜽 + sec 𝜽 का मान ज्ञात कीजिए। 𝟒 𝟑 a) 3𝟓 b) 3 c) 3𝟓 d) 4 𝒔𝒆𝒄𝟐𝜽+𝒄𝒐𝒕𝟐𝜽 58. If 7 𝒔𝒊𝒏𝟐 𝜽 − 𝒄𝒐𝒔𝟐 𝜽 + 𝟐𝒔𝒊𝒏𝜽 = 𝟐, 𝟎° < 𝜽 < 𝟗𝟎°, 𝒕𝒉𝒆𝒏 𝒕𝒉𝒆 𝒗𝒂𝒍𝒖𝒆 𝒐𝒇 𝒊𝒔? 𝒄𝒐𝒔𝒆𝒄𝟐𝜽+𝒕𝒂𝒏𝟐𝜽 यदि 7 𝒔𝒊𝒏𝟐 𝜽 − 𝒄𝒐𝒔𝟐 𝜽 + 𝟐𝒔𝒊𝒏𝜽 = 𝟐, 𝟎° < 𝜽 < 𝟗𝟎° है, तो का मान क्या है ? 𝒔𝒆𝒄𝟐𝜽+𝒄𝒐𝒕𝟐𝜽 𝒄𝒐𝒔𝒆𝒄𝟐𝜽+𝒕𝒂𝒏𝟐𝜽 𝟐√𝟑+𝟏 𝟏(𝟏+𝟐√𝟑) 𝟐 a) b) 1 c) d) (𝟏 + √𝟑) 𝟑 𝟓 𝟓 𝒔𝒆𝒄𝟐𝜽+𝒄𝒐𝒕𝟐𝜽 59. If 14sin²  + 3sin – 5 = 0, 0° <  < 90°, then the value of 𝒄𝒐𝒔𝒆𝒄𝟐𝜽+𝒕𝒂𝒏𝟐𝜽 is: 𝒔𝒆𝒄𝟐𝜽+𝒄𝒐𝒕𝟐𝜽 ;fn 14sin²  + 3sin – 5 = 0, 0° <  < 90° gS] rks dk eku D;k gksxk\ 𝒄𝒐𝒔𝒆𝒄𝟐𝜽+𝒕𝒂𝒏𝟐𝜽 𝟑√𝟑−𝟏 (a) 𝟑 𝟐√𝟑+𝟏 (b) 𝟑 𝟐(𝟏+√𝟑) (c) 𝟓 𝟏+𝟐√𝟑 (d) 𝟓 𝜽 𝜽 𝒔𝒊𝒏𝟐 𝜽 𝒕𝒂𝒏𝟐 +𝒔𝒊𝒏𝟐 𝟐 𝟐 60. If 𝒄𝒐𝒔𝟐 𝜽−𝟑𝒄𝒐𝒔𝜽+𝟐=1 , θ lies in the first quadrant, then the value of is 𝒕𝒂𝒏𝜽+𝒔𝒊𝒏𝜽 𝜽 𝜽 𝒔𝒊𝒏𝟐 𝜽 𝒕𝒂𝒏𝟐 +𝒔𝒊𝒏𝟐 यदि 𝒄𝒐𝒔𝟐 𝜽−𝟑𝒄𝒐𝒔𝜽+𝟐=1, θ पहले चतथ ु ाांश में है, तो 𝟐 𝟐 का मान है? 𝒕𝒂𝒏𝜽+𝒔𝒊𝒏𝜽 𝟐√𝟑 𝟓√𝟑 𝟐√𝟑 𝟕√𝟑 (a) 𝟐𝟕 (b) 𝟐𝟕 (c) (d) 𝟓𝟒 𝟗 61. If 4 − 6cos2 − sin = 0, 00 <  < 900, then the value of cot + tan: 4 − 6cos2 − sin = 0, 00 <  < 900, cot + tan a) 92/5 b) 9/25 c) 32/5 d) 3/25 62. If 8cos² – 2cos – 3 = 0, 0° <  < 90°, then what is the value of 3 tan + cosec + cot? ;fn 8cos² – 2cos – 3 = 0, 0° <  < 90° gS] rks 3 tan + cosec + cot dk eku D;k gS\ (a) 𝟐 √𝟕 𝟒 (b) √𝟕 𝟑 𝟑 (c) √𝟕 𝟒 (d) 𝟒√𝟕 Telegram channel By Gagan Pratap Sir- https://t.me/mathsbygaganpratap Join Full Batch Download Careerwill App- https://bit.ly/CareerwillApp  𝒄𝒐𝒕𝟐𝜽+𝒄𝒐𝒔𝟐𝜽 63. If 11𝒔𝒊𝒏𝟐 𝜽 − 𝒄𝒐𝒔𝟐 𝜽 + 𝟒𝒔𝒊𝒏𝜽 − 𝟒 = 𝟎, 𝟎° < 𝜽 < 𝟗𝟎°, then what is the value of 𝒔𝒆𝒄𝟐𝜽−𝒕𝒂𝒏𝟐𝜽 ? यदि 11𝒔𝒊𝒏𝟐 𝜽 − 𝒄𝒐𝒔𝟐 𝜽 + 𝟒𝒔𝒊𝒏𝜽 − 𝟒 = 𝟎, 𝟎° < 𝜽 < 𝟗𝟎°, तो का मान क्या है ? 𝒄𝒐𝒕𝟐𝜽+𝒄𝒐𝒔𝟐𝜽 𝒔𝒆𝒄𝟐𝜽−𝒕𝒂𝒏𝟐𝜽 𝟏𝟐+𝟕√𝟑 𝟏𝟐+𝟓√𝟑 𝟏𝟎+𝟓√𝟑 𝟏𝟎+𝟕√𝟑 a) b) c) d) 𝟔 𝟑 𝟑 𝟔 𝟏 𝟏 64. If + 𝟏−𝒕𝒂𝒏𝜽 = 4, 0° <  < 90°, then what is the value of cosec + sec + sin ? 𝟏+𝒕𝒂𝒏𝜽 𝟏 𝟏 ;fn + 𝟏−𝒕𝒂𝒏𝜽 = 4, 0° <  < 90°, rks cosec + sec + sin dk eku D;k gS\ 𝟏+𝒕𝒂𝒏𝜽 𝟑+𝟒√𝟐 (a) √𝟔 𝟖√𝟑 (b) 𝟑 𝟑√𝟑 (c) 𝟐 𝟒+𝟑√𝟐 (d) √𝟔 65. If tan2 − 3sec + 3 = 0, 00 <  < 900, then the value of sin + cot is: tan2 − 3sec + 3 = 0, 00 <  < 900 sin + cot 𝟓√𝟑 𝟓√𝟑 a) b) 2√𝟑 c) d) 3√𝟑 𝟔 𝟑 𝟐𝒕𝒂𝒏𝜽−𝒄𝒐𝒔𝜽 66. If tanθ – cotθ = cosecθ 0