Trigonometric Identities Question 312
Question: If $ \alpha $ is a root of $ 25{{\cos }^{2}}\theta +5\cos \theta -12=0 $ , $ \pi /2<\alpha <\pi $ , then $ \sin 2\alpha $ is equal to
[UPSEAT 2001]
Options:
A) $ 24/25 $
B) $ -24/25 $
C) $ 13/18 $
D) $ -13/18 $
Show Answer
Answer:
Correct Answer: B
Solution:
Since a is a root of $ 25{{\cos }^{2}}\theta +5\cos \theta -12=0 $ \ $ 25{{\cos }^{2}}\alpha +5\cos \alpha -12=0 $
Þ $ \cos \alpha =\frac{-5\pm \sqrt{25+1200}}{50} $ $ =\frac{-5\pm 35}{50} $
Þ $ \cos \alpha =-4/5 $ $ [\because \pi /2<\alpha <\pi \Rightarrow \cos \alpha <0] $
$ \therefore $ $ \sin 2\alpha =2\sin \alpha \cos \alpha =-24/25 $ .
BETA
