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Trigonometrical Equations
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જો $0 \le x \le \pi $ અને ${81^{{{\sin }^2}x}} + {81^{{{\cos }^2}x}} = 30$, તો $x =$
A
$\pi /6$
B
$\pi /2$
C
$\pi /4$
D
$3\pi /4$
(JEE MAIN-2021)
Solution
(a) We have, ${81^{{{\sin }^2}x}} + {81^{{{\cos }^2}x}} = 30$
Now check by options, put $x = \frac{\pi }{6}$
then ${(81)^{{{\sin }^2}\pi /6}} + {(81)^{{{\cos }^2}\pi /6}} = 30$
==> ${(81)^{1/4}} + {(81)^{3/4}} = 30$
Hence $(a)$ is the correct answer.
Standard 11
Mathematics
