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

$(1-cos x)(1+cos x)$

On multiplying using the identity

$(a-b)(a+b)=a^{2}-b^{2}$

we get the equation as

$(1-cos x)(1+cosx)=1-cos^{2}x$ $sin ^{2}x +cos^{2}x=1 \Rightarrow cos^{2}x-1= sin^{2}x$