How do you verify the identity $sec^2thetacsc^2theta=sec^2theta+csc^2theta$ ?

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Answer 1 · 2016-09-18T05:23:28

For Proof, see the Explanation below.

$sec^2thetacsc^2theta=1/cos^2theta*1/sin^2theta=1/(cos^2thetasin^2theta)$

$=(cos^2theta+sin^2theta)/(cos^2thetasin^2theta)$

$=cos^2theta/(cos^2thetasin^2theta)+sin^2theta/(cos^2thetasin^2theta)$

$=1/sin^2theta+1/cos^2theta$

$=csc^2theta+sec^2theta$ .

Hence, the Proof.

How do you verify the identity sec^2thetacsc^2theta=sec^2theta+csc^2thetasec^2thetacsc^2theta=sec^2theta+csc^2theta?