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Trigonometrical Equations
hard
समीकरण $32^{\tan ^{2} x}+32^{\sec ^{2} x}=81,0 \leq x \leq \frac{\pi}{4}$ के हलों की संख्या है
A
$3$
B
$1$
C
$0$
D
$2$
(JEE MAIN-2021)
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
Standard 11
Mathematics
