Math, asked by Karankeshri, 6 months ago

Prove that sec^2Q-cos^2Q = sin^2Q(sec^2Q+1)

Answers

Answered by chitluridevicharan

1

Step-by-step explanation:

Take LHS, sec^2Q-cos^2Q

=1/cos^2Q-cos^2Q

=1-cos^4Q/cos^2Q

=(1+cos^2Q)(1-cos^2Q)/cos^2Q

=(1+cos^2Q)(sin^2Q)/cos^2Q

=(1+cos^2Q)*tan^2Q

=tan^2Q+sin^2Q.

Take RHS,sin^2Q(sec^2Q+1)

=sin^2Q(1/cos^2Q+1)

=sin^2Q/cos^2Q+sin^2Q

=tan^2Q+sin^2Q.

LHS=RHS.

Thus proved.

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