667eaf923d4f0f6df48a8e75_##_Trigonometry Practice Sheet (Level 2) Udaan 2025.pdf
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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