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

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Answer 1 · 2018-05-22T19:30:59

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

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

# = 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#