Question

Solve $\sin x+\cos x=1+\sin x\cos x$

Answer 1

Given,

$\sin x+\cos x=1+\sin x\cos x$

Squaring both sides we get,

${\sin }^{2}x+2.\sin x.\cos x+{\cos }^{2}x=1+2\sin x.\cos x+{\cos }^{2}x.{\sin }^{2}x$

or, ${\sin }^{2}x.{\cos }^{2}x=0$ [Since ${\sin }^{2}x+{\cos }^{2}x=1$]

or, $\sin x=0$ or $\cos x=0$

or, $x=n\pi$ or $x=\frac{(2n+1)\pi }{2},n\in N$