Question

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

• A. 3
• B. 1
• C. 0
• D. 2

Answer 1

Answer: (B)

$(32{)}^{{\tan }^{2}x}+(32{)}^{{\sec }^{2}x}=81$
$\Rightarrow (32{)}^{{\tan }^{2}x}+(32{)}^{1+{\tan }^{2}x}=81$
$\Rightarrow (32{)}^{{\tan }^{2}x}=\frac{81}{33}$
In interval $\left[0,\frac{\pi }{4}\right]$ only one solution