Find 3θ if cos2θ - sin2θ = 1/2 , 0° < θ < 90°

We know sin²θ + cos²θ=1

cos²θ=1 - sin²θ

ATQ

cos²θ - sin²θ = \(\frac{1}{2}\)

1 - sin²θ - sin²θ = \(\frac{1}{2}\)

- 2sin²θ = \(\frac{1}{2}\)-1

sin²θ =\(\frac{1}{4}\)

sinθ =\(\frac{1}{2}\) = 30°

3θ = 30×3 = 90°