# How do you solve 1 + sin(x) = cos(x)?

$x = 0$
$1 + \sin \left(x\right) = \cos \left(x\right) \mathmr{and} \cos x - \sin x = 1$. Squaring both sides we get (cosx-sinx)^2=1 or cos^2x+sin^2x -2sinxcosx=1 or 1-sin2x=1 or sin2x=0=sin0;We know $\sin 0 = 0 \therefore 2 x = 0 \mathmr{and} x = 0$[Ans]