Prove that ${\sin ^{ – 1}}\frac{8}{{17}} + {\sin ^{ – 1}}\frac{3}{5} = {\sin ^{ – 1}}\frac{{77}}{{85}}$.
Find the simplified form of
${\cos ^{ – 1}}\left( {\frac{3}{5}\cos x + \frac{4}{5}\sin x} \right)$, where $x \in \left[ {\frac{{ – 3\pi }}{4},\frac{\pi }{4}} \right]$.
[NCERT,Exemplar.2.3,Q.13,Page.36]
Prove that ${\tan ^{ – 1}}\left( {\frac{{\sqrt {1 + {x^2}} + \sqrt {1 – {x^2}} }}{{\sqrt {1 + {x^2}} – \sqrt {1 – {x^2}} }}} \right) = \frac{\pi }{4} + \frac{1}{2}{\cos ^{ – 1}}{x^2}$.
[NCERT,Exemplar.2.3,Q.12,Page.36]
Solve the equation $\cos \left( {{{\tan }^{ – 1}}x} \right) = \sin \left( {{{\cot }^{ – 1}}\frac{3}{4}} \right)$.
[NCERT,Exemplar.2.3,Q.11,Page.36]
Show that $\cos \left( {2{{\tan }^{ – 1}}\frac{1}{7}} \right) = \sin \left( {4{{\tan }^{ – 1}}\frac{1}{3}} \right)$.
[NCERT,Exemplar.2.3,Q.10,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]
Find the value of $\sin \left( {2{{\tan }^{ – 1}}\frac{1}{3}} \right) + \cos \left( {{{\tan }^{ – 1}}2\sqrt 2 } \right)$. [NCERT,Exemplar.2.3,Q.8,Page.36]
Find the real Solution of
${\tan ^{ – 1}}\sqrt {x(x + 1)} + {\sin ^{ – 1}}\sqrt {{x^2} + x + 1} = \frac{\pi }{2}$.
[NCERT,Exemplar.2.3,Q.7,Page.36]
Show that $2{\tan ^{ – 1}}( – 3) = \frac{{ – \pi }}{2} + {\tan ^{ – 1}}\left( {\frac{{ – 4}}{3}} \right)$.
[NCERT,Exemplar.2.3,Q.6,Page.35]