# How do you simplify #(1+cos x) (1-cos x)#?

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Expand the brackets using FOIL , or the method you use.

#rArr (1 + cosx)(1 - cosx) = 1 -cosx + cosx - cos^2 x #

#= 1 - cos^2 x# using the identity

#color(red)(|bar(ul(color(white)(a/a)color(black)( sin^2 x + cos^2 x = 1 )color(white)(a/a)|)))# then

# 1 - cos^2 x = sin^2 x#

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The expression we have fits the **difference of squares** pattern

We know that a difference of squares pattern is equal to

This expression should look familiar. It is derived from the **Pythagorean Identity**

where we can subtract

Thus, this expression is equal to

All we did was use the difference of squares property to our advantage, recognize that the expression we have is similar to the Pythagorean Identity, use the identity, and simplify.

Hope this helps!

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