Question

Prove that:

( sec 4A - 1 ) / ( sec 2A - 1 )

=

tan 4A . cot A

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Answer 1

The answer is, sec2A + tan2A − 2tan

Answer 2

Consider the L.H.S,

=sec4A(1−sin4A)−2tan2A

=sec4A−sec4Asin4A−2tan2A

=sec4A−cos4Asin4A−2tan2A

=sec4A−tan4A−2tan2A

=[(sec2A)2−(tan2A)2]−2tan2A

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

We know that

sec2A−tan2A=1

Therefore,

=sec2A+tan2A−2tan