Trigonometric Identities Question 126
Question: If $ 5\tan \theta =4, $ then $ \frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }= $
[Karnataka CET 1998]
Options:
A) 0
B) 1
C) 1/6
D) 6
Show Answer
Answer:
Correct Answer: C
Solution:
$ 5\tan \theta =4\Rightarrow \tan \theta =\frac{4}{5} $
$ \therefore \sin \theta =\frac{4}{\sqrt{41}} $ and $ \cos \theta =\frac{5}{\sqrt{41}} $ $ \frac{5\sin \theta -3\cos \theta }{5\sin \theta +2\cos \theta }=\frac{5\times \frac{4}{\sqrt{41}}-3\times \frac{5}{\sqrt{41}}}{5\times \frac{4}{\sqrt{41}}+2\times \frac{5}{\sqrt{41}}} $ $ \frac{20-15}{20+10}=\frac{5}{30}=\frac{1}{6} $ .
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