SATHEE: Quantitative Aptitude Ques 41

Quantitative Aptitude Ques 41

Question: If $ \tan A=n\tan B $ and $ \sin A=m,\sin B, $ then the value of $ {{\cos }^{2}}A $ is

Options:

A) $ \frac{m^{2}-1}{n^{2}+1} $

B) $ \frac{m^{2}+1}{n^{2}+1} $

C) $ \frac{m^{2}-1}{n^{2}-1} $

D) $ \frac{m^{2}+1}{n^{2}-1} $

Show Answer

Answer:

Correct Answer: C

Solution:

Given, $ \tan A=n\tan B $

$ \therefore $ $ \cot B=n\cot A $ … (i) and $ \sin A=m,\sin B $

$ \Rightarrow $ $ cosec,B=m,cosec,A $ … (ii) On squaring both sides of Eqs. (i) and (ii) and then subtracting Eq. (i) from Eq. (ii), we get $ cose{c^{2}}B-{{\cot }^{2}}B=m^{2}cose{c^{2}}A-n^{2}{{\cot }^{2}}A $

$ \Rightarrow $ $ \frac{m^{2}-n^{2}{{\cos }^{2}}A}{{{\sin }^{2}}A}=1 $

$ \Rightarrow $ $ m^{2}-n^{2}{{\cos }^{2}}A=1-{{\cos }^{2}}A $

$ \therefore $ $ {{\cos }^{2}}A=\frac{m^{2}-1}{n^{2}-1} $

Quantitative Aptitude Ques 40

Quantitative Aptitude Ques 42

Quantitative Aptitude Ques 41

Question: If $ \tan A=n\tan B $ and $ \sin A=m,\sin B, $ then the value of $ {{\cos }^{2}}A $ is

Options:

Answer:

Solution:

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