Find 3θ if cos2θ - sin2θ = \(\frac{1}{2}\),  0° < θ < 90°

45° 30° 60° 90°

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°