Show that $\tan \left( {\frac{1}{2}{{\sin }^{ – 1}}\frac{3}{4}} \right) = \frac{{4 – \sqrt 7 }}{3}$ and justify why the other value $\frac{{4 + \sqrt 7 }}{3}$ is ignored?[NCERT,Exemplar.2.3,Q.18,Page.37] Uncategorized
Find the value of $4{\tan ^{ – 1}}\frac{1}{5} – {\tan ^{ – 1}}\frac{1}{{239}}$.[NCERT,Exemplar.2.3,Q.17,Page.37] Uncategorized
Prove that ${\tan ^{ – 1}}\frac{1}{4} + {\tan ^{ – 1}}\frac{2}{9} = {\sin ^{ – 1}}\frac{1}{{\sqrt 5 }}$.[NCERT,Exemplar.2.3,Q.16,Page.36] Uncategorized
Show that ${\sin ^{ – 1}}\frac{5}{{13}} + {\cos ^{ – 1}}\frac{3}{5} = {\tan ^{ – 1}}\frac{{63}}{{16}}$.[NCERT,Exemplar.2.3,Q.15,Page.36] Uncategorized
Prove that ${\sin ^{ – 1}}\frac{8}{{17}} + {\sin ^{ – 1}}\frac{3}{5} = {\sin ^{ – 1}}\frac{{77}}{{85}}$.[NCERT,Exemplar.2.3,Q.14,Page.36] Uncategorized
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] Uncategorized
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] Uncategorized
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] Uncategorized
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] Uncategorized
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] Uncategorized
