Trigonometric Equations Question 12
Question: If $ \sin 2\theta =\cos 3\theta $ and $ \theta $ is an acute angle, then $ \sin \theta $ is equal to
[EAMCET 1980]
Options:
A) $ \frac{\sqrt{5}-1}{4} $
B) $ \frac{-\sqrt{5}-1}{4} $
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \sin 2\theta =\cos 3\theta $
$ \Rightarrow $ $ 3\theta =2n\pi \pm ( \frac{\pi }{2}-2\theta ) $
$ \Rightarrow $ $ \theta =\frac{2n\pi }{5}+\frac{\pi }{10} $ or $ \theta =2n\pi -\frac{\pi }{2} $ . Since $ \theta $ is acute Þ $ \theta =\frac{\pi }{10} $
Þ $ \sin \theta =\frac{\sqrt{5}-1}{4} $ .
BETA
