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Question
Prove the following identities:
cosec4 A (1 – cos4 A) – 2 cot2 A = 1
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Solution
cosec4 A (1 – cos4 A) – 2 cot2 A
= cosec4 A (1 – cos2 A) (1 + cos2 A) – 2 cot2 A
= cosec4 A (sin2 A) (1 + cos2 A) – 2 cot2 A
= cosec2 A (1 + cos2 A) – 2 cot2 A
= `cosec^2A + cos^2A/sin^2A - 2cot^2A `
= cosec2 A + cot2 A – 2 cot2 A
= cosec2 A – cot2 A
= 1
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