Question

How do you prove `\cos ^ { 2} x = ( 1- \sin x ) ( 1+ \sin x )`?

Answer 1

I tried this:

Explanation:

You can multiply the two brakets and get:
`cos^2(x)=1+cancel(sin(x))cancel(-sin(x))-sin^2(x)`
`cos^2(x)=1-sin^2(x)`
`cos^2(x)=cos^2(x)`

where `1-sin^2(x)=cos^2(x)`
because you know that:
`sin^2(x)+cos^2(x)=1`