Prove that

Question

1+sinx=cos^2x/1-sinx Thank you?

Answer 1

Given trigonometric identity :

1 + sinx = cos²x / (1-sinx)

Start from left hand side.

1 + sinx

 = (1 + sinx) / 1

Rationalize with (1 - sinx)

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

= (1² - sin²x) / (1 - sinx)

= (1 - sin²x) / (1 - sinx)

Substitute trigonometric identity : 1 - sin²x = cos²x

= (cos²x) / (1 - sinx)

Hence Trigonometric identity 1 + sinx = cos²x / (1-sinx) is proved.