Trigonometric Identities Question 253
Question: If $ \sin (\pi \cos x)=cos(\pi sinx), $ then what is one of the values of $ sin2x $ ?
Options:
A) $ -\frac{1}{4} $
B) $ -\frac{1}{2} $
C) $ -\frac{3}{4} $
D) $ -1 $
Show Answer
Answer:
Correct Answer: C
Solution:
Given that: $ \sin (\pi \cos x)=\cos (\pi \sin x) $ So, $ \cos ( \frac{\pi }{2}-\pi \cos x )=\cos (\pi \sin x) $
$ \Rightarrow \frac{\pi }{2}-\pi \cos x=\pi \sin x $
$ \Rightarrow \sin x+\cos x=\frac{1}{2} $ Squaring both sides, we get $ {{\sin }^{2}}x+{{\cos }^{2}}x+2\sin x\cos x=\frac{1}{4} $
$ \Rightarrow \sin 2x=\frac{1}{4}-1=-\frac{3}{4} $
BETA
