How do you verify the identity $(1+sinalpha)(1-sinalpha)=cos^2alpha$ ?

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Answer 1 · 2017-01-04T21:11:34

see below

$color(red)((1+sinalpha)(1-sinalpha))=cos^2alpha$

apply FOIL to the red bit. you get: $1 - sin alpha + sin alpha - sin^2 alpha = 1 - sin^2 alpha$

then you have the Pythagorean identity to finish it off :)

$1 - sin^2 alpha = cos^2 alpha implies sin^2 alpha + cos^2 alpha = 1$

How do you verify the identity (1+sinalpha)(1-sinalpha)=cos^2alpha(1+sinalpha)(1-sinalpha)=cos^2alpha?