Precalculus
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Find all solutions to the equation where 0 ≤ θ\thetaθ ≤ 2π2\pi2π.
sinθcos(2θ)−sin(2θ)cosθ=22\sin\theta\cos\left(2\theta\right)-\sin\left(2\theta\right)\cos\theta=\frac{\sqrt2}{2}sinθcos(2θ)−sin(2θ)cosθ=22
θ=5π4,7π4\theta=\frac{5\pi}{4},\frac{7\pi}{4}θ=45π,47π
θ=π4,3π4\theta=\frac{\pi}{4},\frac{3\pi}{4}θ=4π,43π
θ=5π4+2πn,7π4+2πn\theta=\frac{5\pi}{4}+2\pi n,\frac{7\pi}{4}+2\pi nθ=45π+2πn,47π+2πn
θ=3π4,7π4\theta=\frac{3\pi}{4},\frac{7\pi}{4}θ=43π,47π