Question

Principal solutions of the equation
$sin2x+cos2x=0$, 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 $sin2x+cos2x=0$
$\Rightarrow sin2x=-cos2x$
$\Rightarrow tan2x=-1$
$[\because \pi <x<2\pi \Rightarrow 2\pi <2x<4\pi$
$\Rightarrow 2x=2\pi +\frac{3\pi }{4},2\pi +\left(\frac{3\pi }{2}+\frac{\pi }{4}\right)$
$\Rightarrow 2x=\frac{11\pi }{8},\frac{15\pi }{4}$
$\Rightarrow x=\frac{11\pi }{8},\frac{15\pi }{8}$