Find the general solution of the trigonometric equation We have to find the general solution of the trigonometric equation  - (cos x - sin x) =$\sqrt2$ And cos x > sin x But how to proceed

HINT:

Another way:

$$\cos x-\sin x=\sqrt2\sin\left(\dfrac\pi4-x\right)$$

$$\cos x+\sin x=\sqrt2\cos\left(\dfrac\pi4-x\right)$$

Write $\dfrac\pi4-x=\dfrac\pi2-2y$

$$\sqrt3\sin2y-\cos2y=1\iff2\sqrt3\sin y\cos y=1+\cos2y=2\cos^2y$$

$$\cos y\left(\tan y-\dfrac1{\sqrt3}\right)=0$$