Question

How do you simplify the expression `cosxsinx-cos^2x`?

Answer 1

`sqrt2cos x.sin (x - pi/4)`

Explanation:

`f(x) = cos x.sin x - cos^2 x = cos x (sin x - cos x) =`
Applying trig identity:
`sin x - cos x = sqrt2sin (x - pi/4)`,
we get:
`f(x) = sqrt2cos x.sin (x - pi/4)`