Question

Prove the following trigonometric identities (secx+tanx)(1-sinx/cosx)=1

Answer 1

Below.

Explanation:

Convert to sin's and cos's:-

(secx + tanx)(1-sinx)/cosx)

= ( 1/ cos x + sinx / cos x) * ( 1 - sin x )/ cos x)

= (1 + sin x) / cos x) * ( 1 - sin x ) / cos x

= (1 - sin^2 x) / cos^2 x

But 1 - sin^2 x = cos^2 x

so we have

cos^2 x / cos^2 x which = 1.