Quantitative Aptitude Ques 2244

Question: What is the value of $ \sin A+\cos A\tan A+\cos A\sin A\cot A? $ [CDS 2012]

Options:

A) $ {{\sin }^{2}}A+\cos A $

B) $ {{\sin }^{2}}A+{{\tan }^{2}}A $

C) $ {{\sin }^{2}}A+{{\cot }^{2}}A $

D) $ cose{c^{2}}A-{{\cot }^{2}}A $

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ \sin A\cos A\tan A+\cos A\sin A\cot A $ $ =\sin A\cos A\frac{\sin A}{\cos A}+\cos A\sin A\frac{\cos A}{\sin A} $ $ ={{\sin }^{2}}A+{{\cos }^{2}}A=1 $ $ [\because {{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1] $ $ =cose{c^{2}}A-{{\cot }^{2}}A $ $ [\because 1+{{\cot }^{2}}\theta =cose{c^{2}}\theta ] $
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