Question

The general solution of the trigonometrical equation $\sin x+\cos x=1$,for n = 0 ,$\pm$1,$\pm$2,.......is given by

• A. x= $2n\pi$
• B. x = $2n\pi +\frac{1}{2}\pi$
• C. x= $n\pi +(-1{)}^n\frac{\pi }{4}-\frac{\pi }{4}$
• D. None of these

Answer 1

The correct option is C x= $n\pi +(-1{)}^n\frac{\pi }{4}-\frac{\pi }{4}$

$\frac{1}{\sqrt{2}}\sin x+\frac{1}{\sqrt{2}}\cos x=\frac{1}{\sqrt{2}}$

$\sin (x+\frac{\pi }{4})=\sin \frac{\pi }{4}$

$x+\frac{\pi }{4}=n\pi +(-1{)}^n\frac{\pi }{4}$

$x=n\pi +(-1{)}^n\frac{\pi }{4}-\frac{\pi }{4}$