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Question

Cosec^4 A(1-cos^4)-2cot^2 A=1

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Solution

L.H.S

cosec^4A(1-cos^4)-2cot^2A

=cosec^4A(1-(1-sin^2A)^2)-2cot^2A

=cosec^4A(1-(1–2sin^2A+sin^4A))-2cot^2A

=cosec^4A(1–1+2sin^2A-sin^4A)-2cot^2A

=cosec^4A(2sin^2A-sin^4A)-2cot^2A

=2.sin^2A.cosec^4A-sin^4A.cosec^4A-2cot^2A

=2cosec^2A-1–2cot^2A

=2(cosec^2A-cot^2A)-1

=2*1–1

=2–1

=1

=R.H.S

Hnece proved.


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