Trigonometric Identities Question 236
Question: If $ 0\le x\le \pi $ and $ {81^{{{\sin }^{2}}x}}+{81^{{{\cos }^{2}}x}}=30, $ then x=
Options:
A) $ \pi /6 $
B) $ \pi /2 $
C) $ \pi /4 $
D) $ 3\pi /4 $
Show Answer
Answer:
Correct Answer: A
Solution:
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 $
$ \Rightarrow {{(81)}^{1/4}}+{{(81)}^{3/4}}=30\Rightarrow 30=30 $
BETA
