The value of $$\tan \alpha + 2\tan (2\alpha ) + 4\tan (4\alpha ) + ... + {2^{n - 1}}\tan ({2^{n - 1}}\alpha ) + {2^n}\cot ({2^n}\alpha )$$ is

$$\tan \left[ {{\pi \over 4} + {1 \over 2}{{\cos }^{ - 1}}\left( {{a \over b}} \right)} \right] + \tan \left[ {{\pi \over 4} - {1 \over 2}{{\cos }^{...

Value of $${\tan ^{ - 1}}\left( {{{\sin 2 - 1} \over {\cos 2}}} \right)$$ is

The solution set of the inequation $${\cos ^{ - 1}}x

For $$y = {\sin ^{ - 1}}\left\{ {{{5x + 12\sqrt {1 - {x^2}} } \over {13}}} \right\};\left| x \right| \le 1$$, if $$a(1 - {x^2}){y_2} + bx{y_1} = 0$$ t...

If $$0 \le A \le {\pi \over 4}$$, then $${\tan ^{ - 1}}\left( {{1 \over 2}\tan 2A} \right) + {\tan ^{ - 1}}(\cot A) + {\tan ^{ - 1}}({\cot ^3}A)$$

The possible values of x, which satisfy the trigonometric equation $${\tan ^{ - 1}}\left( {{{x - 1} \over {x - 2}}} \right) + {\tan ^{ - 1}}\left( {{{...

If $${r^2} = {x^2} + {y^2} + {z^2}$$, then prove that $${\tan ^{ - 1}}\left( {{{yz} \over {rx}}} \right) + {\tan ^{ - 1}}\left( {{{zx} \over {ry}}} \r...