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Question
Prove the following identities:
cosec4 A – cosec2 A = cot4 A + cot2 A
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Solution
L.H.S. = cosec4 A – cosec2 A
= cosec2 A (cosec2 A – 1)
R.H.S. = cot4 A + cot2 A
= cot2 A (cot2 A + 1)
= (cosec2 A – 1) cosec2 A
Thus, L.H.S. = R.H.S.
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