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#