Question

How do you use the double angle or half angle formulas to solve `2 sinx cosx=cos 2x`?

Answer 1

Solve 2sin x.cos x = cos 2x

Ans: `x = pi/8`

Explanation:

Apply the 2 trig identities: 2sin x.cos x = sin 2x.
`cos x = sin (pi/2 - x)`
We have:
`sin 2x = cos 2x = sin (pi/2 - 2x)`
`2x = (pi/2 - 2x)`
`4x = pi/2` --> `x = pi/8`
Check by calculator.
`x = pi/8 = 22^@5` --> 2x = 45 -->
--> sin 2x = 0.71 --> cos 2x = 0.71 .OK