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Question

Prove that sec4A(1sin4A)2tan2A=1.

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Solution

Consider the L.H.S,

=sec4A(1sin4A)2tan2A

=sec4Asec4Asin4A2tan2A

=sec4Asin4Acos4A2tan2A

=sec4Atan4A2tan2A

=[(sec2A)2(tan2A)2]2tan2A

=[(sec2A)(tan2A)][(sec2A)+(tan2A)]2tan2A

We know that

sec2Atan2A=1

Therefore,

=sec2A+tan2A2tan2A

=sec2Atan2A

=1


Hence, proved


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