Trigonometric Identities Question 338
Question: $ {{\cos }^{2}}A{{(3-4{{\cos }^{2}}A)}^{2}}+{{\sin }^{2}}A{{(3-4{{\sin }^{2}}A)}^{2}}= $
Options:
A) $ \cos 4A $
B) $ \sin 4A $
C) 1
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ {{\cos }^{2}}A{{(3-4{{\cos }^{2}}A)}^{2}}+{{\sin }^{2}}A{{(3-4{{\sin }^{2}}A)}^{2}} $ $ ={{(3\cos A-4{{\cos }^{3}}A)}^{2}}+{{(3\sin A-4{{\sin }^{3}}A)}^{2}} $ $ ={{(\cos 3A)}^{2}}+{{(\sin 3A)}^{2}}=1 $ . Trick: Put $ A=\frac{\pi }{2},0^{o} $ , the value of expression remains 1, therefore it is independent of A and is equal to 1.
BETA
