SATHEE: Quantitative Aptitude Ques 86

Quantitative Aptitude Ques 86

Question: If $ \alpha $ is an acute angle and $ 2\sin \alpha +15cos^{2}\alpha =7, $ then the value of cot $ \alpha $ is

Options:

A) $ \frac{5}{4} $

B) $ \frac{4}{3} $

C) $ \frac{3}{4} $

D) $ \frac{4}{5} $

Show Answer

Answer:

Correct Answer: C

Solution:

Here, $ 2\sin \alpha +15{{\cos }^{2}}\alpha =7 $

$ \Rightarrow $ $ 2\sin \alpha +15,(1-{{\sin }^{2}}\alpha )-7=0 $

$ \Rightarrow $ $ 2\sin \alpha +15-15{{\sin }^{2}}\alpha -7=0 $

$ \Rightarrow $ $ 15{{\sin }^{2}}\alpha -2\sin \alpha -8=0 $

$ \Rightarrow $ $ 15{{\sin }^{2}}\alpha +10\sin \alpha -12sin\alpha -8=0 $

$ \Rightarrow $ $ 5sin\alpha ,(3\sin \alpha +2)-4,(3\sin \alpha +2)=0 $

$ \Rightarrow $ $ (5\sin \alpha -4)(3\sin \alpha +2)=0 $
$ \Rightarrow $ $ \sin \alpha =\frac{4}{5} $

$ \therefore $ $ \cot \alpha =\frac{3}{4} $

Quantitative Aptitude Ques 85

Quantitative Aptitude Ques 87

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