How to verify the identity cos(x) + (sin^2 x )/(1+cosx) = 1?

1 Answer
May 22, 2018

See below for full trig identity proof. Basically, you need to substitute and factor sin^2x = 1-cos^2x.

Explanation:

Left side:
cosx + frac{sin^2x}{1+cosx}

Remember and substitute the Pythagorean Trigonometric Identity

= cosx + frac{1-cos^2x}{1+cosx}

Factor the numerator of the fraction:

= cosx + frac{(1-cosx)(1+cosx)}{(1+cosx)}

Simplify by cancelling:
= cosx + frac{(1-cosx)cancel((1+cosx))}{cancel((1+cosx))}

= color(red)(cosx) + (1-color(red)(cosx))

= 1