If $2{\tan ^{ – 1}}(\cos \theta ) = {\tan ^{ – 1}}(2{\mathop{\rm cosec}\nolimits} \theta )$, then show that $\theta = \frac{\pi }{4}$, where $n$ is any integer.
[NCERT,Exemplar.2.3,Q.9,Page.36]

If $2{\tan ^{ – 1}}(\cos \theta ) = {\tan ^{ – 1}}(2{\mathop{\rm cosec}\nolimits} \theta )$, then show that $\theta = \frac{\pi }{4}$, where $n$ is any integer.
[NCERT,Exemplar.2.3,Q.9,Page.36]

We have, $2{\tan ^{ – 1}}(\cos \theta ) = {\tan ^{ – 1}}(2{\mathop{\rm cosec}\nolimits} \theta )$
$ \Rightarrow $${\tan ^{ – 1}}\left( {\frac{{2\cos \theta }}{{1 – {{\cos }^2}\theta }}} \right) = {\tan ^{ – 1}}(2{\mathop{\rm cosec}\nolimits} \theta )$

$ \Rightarrow \left( {\frac{{2\cos \theta }}{{{{\sin }^2}\theta }}} \right) = (2{\mathop{\rm cosec}\nolimits} \theta )$
$ \Rightarrow (\cot \theta \cdot 2{\mathop{\rm cosec}\nolimits} \theta ) = (2{\mathop{\rm cosec}\nolimits} \theta ) \Rightarrow \cot \theta = 1$

$ \Rightarrow $$\cot \theta = \cot \frac{\pi }{4} \Rightarrow \theta = \frac{\pi }{4}$

Buy Best Mathematics E-Books Visit : https://mathstudy.in/

Buy Mathematics Formula Book for Class XI,XII,JEE and other Engineering Competition Exam https://mathstudy.in/product/mathematics-formula-book/

Buy Mathematics Workbook for Class XII ( Fully Solved ) : https://mathstudy.in/product/work-book-class-xii-c-b-s-e-fully-solved/

Buy Mathematics Chapter Tests for Class XII ( Fully Solved) : https://mathstudy.in/product/mathematics-chapter-tests-class-xii-c-b-s-e/

Buy Objective Type Question Bank Class XII (Fully Solved ) : https://mathstudy.in/product/objective-type-question-bank-for-mathematics-class-xii-c-b-s-e/