Question:
The number of solutions of the equation
$32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4}$ is :
Correct Option: , 2
Solution:
$(32)^{\tan ^{2} x}+(32)^{\sec ^{2} x}=81$
$\Rightarrow(32)^{\tan ^{2} x}+(32)^{1+\tan ^{2} x}=81$
$\Rightarrow(32)^{\tan ^{2} x}=\frac{81}{33}$
In interval $\left[0, \frac{\pi}{4}\right]$ only one solution