Question

Which of the following is not the general solution of $2^{{\cos }^{2}x}+1={3.2}^{-{\sin }^{2}x}$ ?

• A. $n\pi ,nϵz$
• B. $(n+\frac{1}{2})\pi ,nϵz$
• C. $(n-\frac{1}{2})\pi ,nϵz$
• D. None of these

Answer 1

The correct option is A $n\pi ,nϵz$

$\Rightarrow 2^{{\cos }^{2}x}+1={3.2}^{-{\sin }^{2}x}$

$\Rightarrow 2^{1-{\sin }^{2}x}+1={3.2}^{-{\sin }^{2}x}$

$\Rightarrow {2.2}^{-{\sin }^{2}x}+1={3.2}^{-{\sin }^{2}x}$

$Let,2^{-{\sin }^{2}x}=k$

$\Rightarrow 2k+1=3k$

$\Rightarrow k=1$

$\Rightarrow 2^{-{\sin }^{2}x}=1=2^0$

$\Rightarrow \sin x=0$

$\Rightarrow x=n\pi$