Question

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Answer 1

$\cos^2x+\sin x=\sqrt{2}\times \sin(x+\frac{\pi}{4})\\ \cos^2x+\sin x=\sqrt{2}\times (\sin x\cos\frac{\pi}{4}+\cos x\sin\frac{\pi}{4})\\ \cos^2x+\sin x=\sqrt{2}\times(\frac{1}{\sqrt{2}}\sin x+\frac{1}{\sqrt{2}}\cos x)\\ \cos^2x+\sin x=\sin x+\cos x\\ \cos^2x-\cos x=0\\ \cos x(\cos x-1)=0\\ x_1=\frac{\pi}{2}+\pi n,n \in Z\\ x_2=2\pi n,n \in Z$