Question

Solve the equation $\sin x+\cos x=1$.

Answer 1

Solve -

$(sinx+cosx)=1$

squaring both sides, we get

$(sinx+cosx{)}^2=1^2$

$=si{n}^{2}x+2sinxcosx+co{s}^{2}x=1$

$[\because si{n}^{2}x+co{s}^{2}x=1]$

$=1+2sinxcosx=1$

$=2sinxcosx=0$

$=sin2x=0$

$\Rightarrow x=2n\pi ,\frac{\pi }{2}+2\pi n$ where n is an integer

$\Rightarrow x=2n\pi ,\frac{\pi }{2}+2\pi n$