Q. Total number of solution of $16^{\cos ^2 x}+16^{\sin ^2 x}=10$ in $x \in[0,3 \pi]$ is equal to-
Trigonometric Functions
Solution:
$16^{\cos ^2 x}+16^{1-\cos ^2 x}=10$
Let $16^{\cos ^2 x}=y, y+\frac{16}{y}=10, y^2-10 y+16=0$
$\Rightarrow y=2,8 \Rightarrow 16^{\cos ^2 x}=2,8 \Rightarrow \cos ^2 x=\frac{1}{4}, \frac{3}{4}$
