prove that (secx+tanx)(1-sinx/cosx)=1

Answer 1

The trigonometric equation is (secx+tanx)((1-sinx)/cosx)) = 1.

Left hand side identity : (secx+tanx)((1-sinx)/cosx))

Reciprocal identity : sec x = 1/cos x

Ratio identity : tan x = sinx/cos x

= ((1/cosx)+(sinx/cosx))((1- sinx)/cosx)

= ((1+ sinx)/cosx)((1- sinx)/cosx)

= ((1- sin²x)/cos²x)                      (Since  (a+b)(a-b) = a² - b² )

Pythagorean identity: cos²x = 1- sin²x.

=cos²x/cos²x

=1

= Right hand side identity.