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Only 5 and 6 q. no
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cosec^6A – cot^6A – 3 cot^2A cosec^2A
= (cosec^2A)^3 – (cot^2A)^3 – 3 cot^2A cosec^2A
= {(cosec^2A – cot^2A) ((cosec^2A)^2 + (cot^2A)^2 + cosec^2A cot^2A)}
= {1 ((cosec^2A)^2 + (cot^2A)^2 – 2 cosec^2A cot^2A + 2 cosec^2A cot^2A + cosec^2A cot^2A)} – 3 cot^2A cosec^2A
= {(cosec^2A – cot^2A)2 + 3 cosec^2A cot^2A} – 3 cosec^2A cot^2A
= (cosec^2A – cot^2A)^2
= (1)^2
= 1
Hence,
cosec^2A – cot^6A – 3 cot^2A cosec^2A = 1
⇒ cosec^2A - cot^6A =1 + 3 cosec^2A cot^2A
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