Question

If $\sin x+\cos x=\sqrt{y+\frac{1}{y}}$ for $x\in [0,\pi ]$, then

• A. $x=\frac{\pi }{4}$
• B. $y=0$
• C. $y=1$
• D. $x=\frac{3\pi }{4}$

Answer 1

Answer: (A), (C)

The correct options are
A $x=\frac{\pi }{4}$
C $y=1$

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

And min $\sqrt{y+\frac{1}{y}}=\sqrt{2}$

Therefore solution when $\sin x+\cos x=\sqrt{2}\Rightarrow x=\frac{\pi }{4}$

$\Rightarrow y=1$