1. Tardigrade
  2. Question
  3. Mathematics
  4. The number of solutions of the equation 32 tan 2 x+32 sec 2 x=81,0 ≤ x ≤ (π/4) is :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The number of solutions of the equation $32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4}$ is :

JEE MainJEE Main 2021Trigonometric Functions

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