JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of solutions of the equation \(32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4}\) is :
- A \(3\)
- B \(1\)
- C \(0\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\((32)^{\tan ^{2} x}+(32)^{\sec ^{2} x}=81\) \(\Rightarrow(32)^{\tan ^{2} x}+(32)^{1+\tan ^{2} x}=81\) \(\Rightarrow(32)^{\tan ^{2} x}=\frac{81}{33}\) In interval \(\left[0, \frac{\pi}{4}\right]\) only one solution
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