Trigonometry Practice Sheet (Level 2) UDAAN 2025 PDF

1 UDAAN 2025 TRIGONOMETRY (Level - 02)...

1 UDAAN 2025 TRIGONOMETRY (Level - 02) Practice Sheet Prove the following trigonometric identities: 10. If a cos  + b sin  = m and a sin  − b cos  = n, 1 + cos  + sin  1 + sin  1. = prove that a + b = m + n. 2 2 2 2 1 + cos  − sin  cos  11. If cos A + cos2 A = 1, prove that sin 2 A + sin 4 A = 1 sin  − cos  + 1 1 2. = 2 2  1 + sin 2   sin  + cos  − 1 sec  − tan   1   1  12.  tan  +  + tan  −  = 2  2  [CBSE 2001, NCERT]  cos    cos    1 − sin   3. ( sin  + cos )( tan  + cot ) = sec + cosec  13. ( sec A + tan A − 1)( sec A − tan A + 1) = 2 tan A [NCERT Exemplar] 14. (1 + cot A − cosec A)(1 + tan A + sec A) = 2 1 1 1 1 4. − = − sec A + tan A cos A cos A sec A − tan A cos A cosec A − sin A sec A [CBSE 2005] 15. = cosec A − sec A cos A + sin A tan A tan A 5. − = 2cosec A tan A cot A 1 + sec A 1 − sec A 16. + = sin A cos A ( ) ( ) 2 2 [NCERT Exemplar] 1 + tan 2 A 1 + cot 2 A 2 6. If cosec  = 2x and cot  = , find the value of x 17. (1 + cot A + tan A)( sin A − cos A)  1  sec A cosec A 2  x2 − 2 . ` [CBSE 2010] = − = sin A tan A − cot A cos A  x  cosec A sec 2 A 2 [CBSE 2008] 7. If cosec  + cot  = m and cosec  − cot  = n, prove 18. If tan  + cot  = 2, find the value of tan 2  + cot 2 . that mn = 1. tan 3  cot 3  8. + = sec  cosec  − 2sin  cos  1 + tan 2  1 + cot 2  9. If x = a cos3 , y = b sin 3 , prove that 2/3 2/3  x  y   +  = 1. a b  2 Answer Key 1. (Prove) 10. (Prove) 2. (Prove) 11. (Prove) 3. (Prove) 12. (Prove) 4. (Prove) 13. (Prove) 5. (Prove) 14. (Prove) 6. (Prove) 15. (Prove) 7. (Prove) 16. (Prove) 8. (Prove) 17. (Prove) 9. (Prove) 18. (Prove) PW Web/App - https://smart.link/7wwosivoicgd4 Library- https://smart.link/sdfez8ejd80if