Question

How do you simplify `sqrt(cosalphasin^2alpha)-sqrt(cos^3alpha)`?

Answer 1

`= sqrt(2a).sin (a + pi/4)`

Explanation:

`P = sqrt(cos a.sin^2 a) - sqrt(cos^3 a) =`
`= sin a.sqrta - cos a.sqrt a = sqrt a(sin a - cos a) =`
Since `(sin a - cos a) = sqrt2sin (a + pi/4)`, there for:
`P = sqrt(2a).sin (a + pi/4)`