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

Below.

Step-by-step 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.