Question

How do you verify `(1+cosx)(1-cosx) = sin^2 x`?

Answer 1

See proof below

Explanation:

Notice, `\sin^2x+\cos^2x=1`

Now, consider LHS, as follows

`LHS=(1+\cos x)(1-\cos x)`

`=1^2-(cos x)^2`

`=1-\cos^2x`

`=\sin^2 x`

`=RHS`

Proved.

Answer 2

`"see explanation"`

Explanation:

`"using the "color(blue)"trigonometric identity"`

`•color(white)(x)sin^2x+cos^2x=1`

`"consider the expansion of the left side"`

`1cancel(-cosx)cancel(+cosx)-cos^2x`

`=1-cos^2x`

`=sin^2x=" right side "rArr"verified"`