Trigonometric Identities Question 138
Question: $ (m+2)\sin \theta +(2m-1)\cos \theta =2m+1, $ if
Options:
A) $ \tan \theta =\frac{3}{4} $
B) $ \tan \theta =\frac{4}{3} $
C) $ \tan \theta =\frac{2m}{m^{2}+1} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Squaring the given relation and putting $ \tan \theta =t, $ $ {{(m+2)}^{2}},t^{2}+2(m+2),(2m-1)t+{{(2m-1)}^{2}}={{(2m+1)}^{2}},(1+t^{2}) $
$ \Rightarrow ,3,(1-m^{2}),t^{2}+(4m^{2}+6m-4),t-8m=0 $
$ \Rightarrow ,(3t-4),[(1-m^{2}),t+2m]=0 $ , which is true if $ t=\tan \theta =\frac{4}{3} $ or $ \tan \theta =\frac{2m}{m^{2}-1} $ .
BETA
