Question

The general solution of the equation $2^{\cos 2x}+1={3.2}^{-\sin x}$ is

• A. $n\pi$
• B. $n\pi -\pi$
• C. $n\pi +\pi$
• D. None of these

Answer 1

Answer: (A)

Given equation is $2^{\cos 2x}+1={3.2}^{-\sin x}$ By taking option [a] Let $x=n\pi$ When $n=1,x=\pi$
$\therefore$ $2^{\cos 2\pi }+1={3.2}^{-\sin x}$
$\Rightarrow$ $2+1={3.2}^0\Rightarrow 3=3$ When $n=2,x=2\pi$
$\therefore$ $2^{\cos 4\pi }+1={3.2}^{-\sin 2\pi }$
$\Rightarrow$ $2^1+1={3.2}^0$
$\Rightarrow$ $3=3$ Hence, option is correct.