Question

How do you express sin x/2 in terms of cos x using the double angle identity?

Answer 1

Express sin (x/2) in terms of cos x.

Ans: `sin (x /2) = sqrt((1 - cos x)/2)`

Explanation:

By applying the trig identity: `cos 2a = 1 - 2sin^2 a`, we get:
`cos x = 1 - 2sin^2 (x/2)`
`2sin^2 (x/2) = 1 - cos x`
`sin^2 (x/2) = (1 - cos x)/2`
`sin (x/2) = +- sqrt((1 - cos x)/2)`