Get Answers to all your Questions

header-bg qa

The value of is \cot \left (cosec^{-1}\frac{5}{3} +\tan ^{-1}\frac{2}{3}\right )

  • Option 1)


  • Option 2)


  • Option 3)


  • Option 4)



Answers (1)

As we learnt in 

Results of Compound Angles -

\cot \left ( A+B \right )= \frac{\cot A\cot B-1}{\cot A+\cot B}

- wherein

Where A and B are two angles.


 \cot \left (cosec^{-1}\frac{5}{3} +tan^{-1}\frac{2}{3} \right ) = \frac{cot\left ( cosec^{-1}\frac{5}{3} \right )\cot \left ( tan^{-1} \frac{2}{3}\right )-1} {cot \:cosec ^{-1}\frac{5}{3}+\cot \: \tan ^{-1}\frac{2}{3}}

Now    \cot cosec^{-1} \frac{5}{3}=\frac{4}{3}                \left [ cosec \theta = \frac{5}{3} \Rightarrow sin\theta=\frac{3}{5},\ cos\theta=\frac{4}{5},\ cot\theta=\frac{4}{3} \right ]

Thus expression becomes 

\frac{\frac{4}{3}\times \frac{3}{2}-1}{\frac{4}{3}+\frac{3}{2}}                                \left[\cot tan^{-1}\frac{2}{3}=\frac{2}{3} \right ]


Option 1)



Option 2)



Option 3)



Option 4)



Posted by

Sabhrant Ambastha

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE