Trigonometric Identities Question 35
Question: If $\sin \theta=3 \sin (\theta+2 \alpha)$, then the value of $\tan (\theta+\alpha)+2 \tan \alpha$ is
Options:
A) 3
B) 2
C) $ -1 $
D) 0
Show Answer
Answer:
Correct Answer: D
Solution:
$ \sin \theta =3\sin (\theta +2\alpha )\Rightarrow \sin (\theta +\alpha -\alpha )=3\sin $ $ (\theta +\alpha +\alpha ) $
$ \Rightarrow \sin (\theta +\alpha )\cos \alpha -\cos (\theta +\alpha )\sin \alpha $ $ =3\sin (\theta +\alpha )\cos \alpha +3\cos (\theta +\alpha )\sin \alpha $
$ \Rightarrow ,-2\sin (\theta +\alpha )\cos \alpha =4\cos (\theta +\alpha )sin\alpha $
$ \Rightarrow \frac{-\sin (\theta +\alpha )}{\cos (\theta +\alpha )}=\frac{2\sin \alpha }{\cos \alpha }\Rightarrow \tan (\theta +\alpha )+2\tan \alpha =0 $
BETA
