Precalculus
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Find all solutions to the equation.
(cosθ+sinθ)(cosθ−sinθ)=−12\left(\cos\theta+\sin\theta\right)\left(\cos\theta-\sin\theta\right)=-\frac12(cosθ+sinθ)(cosθ−sinθ)=−21
θ=5π12+2πn,7π12+2πn\theta=\frac{5\pi}{12}+2\pi n,\frac{7\pi}{12}+2\pi nθ=125π+2πn,127π+2πn
θ=2π3+2πn,4π3+2πn\theta=\frac{2\pi}{3}+2\pi n,\frac{4\pi}{3}+2\pi nθ=32π+2πn,34π+2πn
θ=π3+2πn,2π3+2πn\theta=\frac{\pi}{3}+2\pi n,\frac{2\pi}{3}+2\pi nθ=3π+2πn,32π+2πn
θ=π3+πn,2π3+πn\theta=\frac{\pi}{3}+\pi n,\frac{2\pi}{3}+\pi nθ=3π+πn,32π+πn