Trigonometry Formula & Questions PDF

TRIGNOMETRY Formula 1 + sinA cosecA + 1 secA + tanA = secA + tanA = = 1 – sinA cosecA – 1 secA – tanA 1 – si...

TRIGNOMETRY Formula 1 + sinA cosecA + 1 secA + tanA = secA + tanA = = 1 – sinA cosecA – 1 secA – tanA 1 – sinA cosecA – 1 secA – tanA = secA – tanA = = 1 + sinA cosecA + 1 secA + tanA 1 + cosA secA + 1 cosecA + cotA = cosecA + cotA = = 1 – cosA secA – 1 cosecA – cotA 1 – cosA secA – 1 cosecA – cotA = cosecA – cotA = = 1 + cosA secA + 1 cosecA + cotA 1 – cosA 1. If = x, then x = ? 1 + cosA (a) (cotA + cosecA)2 (b) (cotA – cosecA)2 (c) cotA – cosecA (d) cotA + cosecA 1 + cosA 2. If = x, then x = ? 1 – cosA cot 2 A cot 2 A tan 2 A tan 2 A (a) 2 (b) 2 (c) 2 (d) 2 secA – 1 secA + 1 secA + 1 secA – 1 1 – sinA 3. If = x, then x = ? 1 + sinA (a) (cosecA – cotA)2 (b) secA – tanA (c) (secA – tanA)2 (d) cosecA – cotA 1  cosA 4. =? 1 – sinA (a) (secA – tanA) (b) (secA + tanA) (c) secA + tanA  (d) secA – tanA      cotθ + cosθ 5. If 1 + = ?, 0° < θ < 90° cotθ – cosθ (a) 1 – sec θ + tan θ (b) 1 – sec θ – tan θ (c) 1 + sec θ – tan θ (d) 1 + sec θ + tan θ Type –14 ormula tanθ + secθ –1 1 + sin θ tanθ – secθ +1 = sec θ + tan θ = cos θ tanθ – secθ +1 1 – sinθ tanθ + secθ –1 = sec θ – tan θ = cosθ cotθ + cosecθ – 1 1 + cosθ cotθ – cosecθ +1 = cosec θ + cot θ = sinθ cotθ – cosecθ +1 1 – cosθ cotθ + cosecθ – 1 = cosec θ – cot θ = sinθ tanθ + secθ – 1 1. Find the value of. tanθ – secθ +1 1 + sinθ 1 + tanθ 1 + cosθ 1 + cotθ (a) (b) (c) (d) cosθ cotθ sinθ tanθ 2   tanθ – secθ +1 1 2.   secθ = , then k = ?  tan θ + secθ – 1  k (a) 1 + sin θ (b) 1 – cos θ (c) 1 + cos θ (d) 1 – sin θ 1+ secθ – tanθ cosθ 3. =? 1+ secθ + tanθ1 – sinθ (a) 1 (b) 2 (c) tan θ (d) cos θ  secθ – tanθ +1 4. Find the value of  1 + secθ + tanθ  × cosθ   1 – sinθ (a) 1 – sin θ (b) (c) sin θ + 1 (d) sin θ – 1 cosθ secθ + tanθ + 1 5. If x cos θ = 1 + sin θ then find the value of secθ – tanθ + 1 1 (a) (b) –x (c) x (d) x+1 x 1 + sinθ secθ + tanθ +1 6. If x = then find cosθ tanθ – secθ – 1 1 1 (a) x (b) –x (c) (d) – x x 3  cotθ + cosecθ – 1 7. Find the value of cotθ – cosecθ +1 1 + cosθ 1 – cosθ 1 + sinθ cosθ – 1 (a) (b) (c) (d) sinθ sinθ cosθ sinθ cosecθ + cotθ +1 8. Find the value of cosecθ – cotθ +1 1 + cosθ 1 + cosθ 1 – cosθ (a) (b) (c) (d) 1 + cos θ cosθ sinθ sinθ cosecθ – cotθ + 1 9. =? 1 + cosecθ + cotθ (a) cot θ – cosec θ (b) cos θ – sin θ (c) cot θ + cosec θ (d) cosec θ – cot θ cotθ – cosecθ – 1 10. Find the value of cotθ + cosecθ +1 1 + cosθ 1 – cosθ cotθ +1 cosθ – 1 (a) (b) (c) (d) sinθ sinθ cosecθ sinθ 1 sinθ cosecθ – cotθ +1 11. If = , then find x 1 – cosθ 1 + cosecθ + cotθ (a) x (b) x – 1 (c) x+1 (d) x² – 1 4  Type – 15 Formula sinθ – cosθ +1 1 + sinθ sinθ + cosθ –1 = sec θ + tan θ = cosθ sinθ + cosθ –1 1 – sinθ sinθ – cosθ +1 = sec θ – tan θ = cosθ cosθ – sinθ +1 1 + cosθ cosθ + sinθ – 1 = cosec θ + cot θ = sinθ cosθ + sinθ – 1 1 – cosθ cosθ – sinθ +1 = cosec θ – cot θ = sinθ sinx – cosx + 1 12. Find the value of sinx + cosx – 1 sinx – 1 sinx + 1 sinx – 1 sinx + 1 (a) (b) (c) (d) cosx cosx cosx + 1 cosx + 1 5  sinθ – cosθ + 1 sinθ + 1 13. Find the value of – sinθ + cosθ – 1 cosθ (a) 0 (b) 1 (c) 2 sin θ (d) 2 cos θ sinθ + cosθ – 1 1 + sinθ 14. Find the value of × sinθ – cosθ + 1 1 – sinθ (a) – 2 (b) 2 (c) –1 (d) 1 sinθ + cosθ – 1 tan²θ(cosec²θ – 1) 15. Find the value of × sinθ – cosθ +1 secθ – tanθ 1 (a) 1 (b) 0 (c) –1 (d) 2 1 + sinθ – cosθ  1 + sinθ + cosθ  16. If    +   = 4, θ = ? 1 + sinθ + cosθ  1 + sinθ – cosθ  (a) 90° (b) 60° (c) 45° (d) 30° 6  t 7