If 0 le x le pi and {81^{{{sin }^2}x}} + {81 | vedclass

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Question

(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}} +

Vedclass · Accepted Answer

$\pi /6$

Vedclass · Answer

(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.

If $0 \le x \le \pi $ and ${81^{{{\sin }^2}x}} + {81^{{{\cos }^2}x}} = 30$, then $x =$

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