solving trigonometric equation $3^{\sin^2(x)}+3^{\cos^2(x)}=4$ Please help me to solve this trigonometric equation.

$$3^{\sin^2(x)}+3^{\cos^2(x)}=4.$$


As $\sin^2x+\cos^2x=1$
Let $3^{\cos^2x}=a$
$\displaystyle 3^{\sin^2x}=3^{1-\cos^2x}=\frac3{3^{\cos^2x}}=\frac3a$
So,we have $\displaystyle \frac3a+a=4\iff a^2-4a+3=0\iff a=1,3$
If $a=1,$ $3^{\cos^2x}=1=3^0\iff \cos^2x=0\iff \cos x=0,x=(2n+1)\frac\pi2$
If $a=3,$ $3^{\cos^2x}=3=3^1\iff \cos^2x=1\iff \sin x=0,x=n\pi=2n\frac\pi2$ where $n$ is any integer
So, the answer reduces to any [integral] multiple of $\frac\pi2,$ right?
