Question

Principal solutions of the equation
$sin\,2x+cos\,2x =0$, where $\pi < x < 2\pi$ are

• A. $ \frac{7 \pi}{8}, \frac{11 \pi}{8}$
• B. $ \frac{9 \pi}{8}, \frac{13 \pi}{8}$
• C. $\frac{11 \pi}{8}, \frac{15 \pi}{8}$
• D. $ \frac{15 \pi}{8}, \frac{19 \pi}{8}$

Answer 1

Answer: (C)

Given equation is $sin 2 x+cos 2 x=0$
$\Rightarrow sin 2 x=-cos \,2 x $
$\Rightarrow tan 2 x=-1 $
$[\because \pi<\,x<\,2 \pi \Rightarrow 2 \pi<\,2 x<\,4 \pi$
$\Rightarrow 2 x=2 \pi+\frac{3 \pi}{4}, 2 \pi+\left(\frac{3 \pi}{2}+\frac{\pi}{4}\right)$
$\Rightarrow 2 x=\frac{11 \pi}{8}, \frac{15 \pi}{4}$
$\Rightarrow x=\frac{11 \pi}{8}, \frac{15 \pi}{8}$