Question

Complete the proof of the identity by choosing the Rule that justifies each step.(sec^2x-1) cosx = sin^2x secxTo see a detailed description of a Rule, select the More Information Button to the right of the Rule.

Answer 1

From the question we are to complete the proof

$(sec^2x-1)\cos x=\sin ^2x\sec x$

Solving LHS

By applying Pythagorean rule

$1+\tan ^2x=\sec ^2x$

This implies

$\tan ^2x=\sec ^2x-1$

Therefore we have

$(\sec ^2x-1)\cos x=\tan ^2x\cos x$