Discussion Forum



1)

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:

Option C

Explanation:

Given equation is $\sin 2x+\cos 2x$=0

$\Rightarrow$  sin 2x=-cos 2x

$\Rightarrow$ tan 2x=-1

   $[\because \pi <x<2 \pi\Rightarrow2 \pi <2x <4\pi]$

  $\Rightarrow$       2x=  $2\pi+\frac{3 \pi}{4},2 \pi +\left( \frac{3 \pi}{2}+\frac{\pi}{4}\right)$

 $\Rightarrow$       $2x= \frac{11 \pi}{8}, \frac{15 \pi}{4}$

 $\Rightarrow$     x= $\frac{11\pi}{8},\frac{15 \pi}{8}$