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Prove the following identities (1-17), 1. sec* e – sec² 0 = tan' 0 + tan? 0, 2. sin 0+ cos° 0 = 1-3 sin? 6 cos 0, 3. (cosec 0- sin 0) (sec 0 – cos 0) (tan 0 + cot 0) = 1, 4. cosec 0 (sec 0 – 1) – cot 0 (1 - cos 0), %3D, = tan 0 - sin 0, 5., 1- sin A cos A, sin A – cos A, cos A (sec A - cosec A) sin A + cos A, = sin A, COS, tan A, 6., 1- cot A, cot A, 1- tan A, (sec A cosec A+1), %3D, 17 sin° A+ cos° A sin° A – cos³ A, sin A + cos A, - CO, = 2, sin A - cosA, 8. (sec A sec B+ tan A tan B) – (sec A tan B+ tan A sec B) = 1, 1+ cos 0+sin 0, 1+ cos 0- sin 0, 9., cos e, 1- sin 0, 10. V1- sin 0, 1+ sin 0, 1+sin 0, 1- sin 0, 2, cos e where<0<n, Cos 0', cot e, tan 0, 1 + tan e 1+ cot? e, sin² e, 1+ cot 0, 11., 1-2 sin? 0 cos² 0, CoS, %3D, sin 0 cos 0, cos 0, 12. 1-, = sin 0 cos 0, 1+ tan 0, 1, cosec 0- sin? 0, 1- sin° 0 cos² o, 2+ sin 0 cos 0, sin 0 cos 0, %3D, 13., sec? e- cos? 0, -COS, 14. (1+ tan a tan B)² + (tan a - tan B) = sec" a sec B, = sin? 0 cos 0, St realme SeShot by ayusH PHOtogaapHy, %3D, 15. (1 + cot 0 + tan 0) (sin 0-cos 0), Ise