Trigonometric Identities Question 28
Question: If $ \frac{\pi }{2}<\alpha <\pi ,,\pi <\beta <\frac{3\pi }{2}; $ $ \sin \alpha =\frac{15}{17} $ and $ \tan \beta =\frac{12}{5} $ , then the value of $ \sin (\beta -\alpha ) $ is
[Roorkee 2000]
Options:
A) -171/221
B) -21/221
C) 21/221
D) 171/221
Show Answer
Answer:
Correct Answer: D
Solution:
Given, $ \sin \alpha =\frac{15}{17},\tan \beta =\frac{12}{5} $
$ \Rightarrow \cos \alpha =\frac{8}{17},\sin \beta =\frac{12}{13} $ and $ \cos \beta =-\frac{5}{13} $
Þ $ \pi <\beta <\frac{3\pi }{2} $ ,
$ \therefore \cos \beta =-\frac{5}{13} $ $ \sin (\beta -\alpha )=\sin \beta \cos \alpha -\cos \beta \sin \alpha $ = $ \frac{171}{221} $ .
BETA
