1

IIT-JEE 1998

Subjective
Prove that $$\tan \,\alpha + 2\tan 2\alpha + 4\tan 4\alpha + 8\cot 8\alpha = \cot \alpha $$

Answer

Solve it.
2

IIT-JEE 1997

Subjective
Prove that $$\sum\limits_{k = 1}^{n - 1} {\left( {n - k} \right)\,\cos \,{{2k\pi } \over n} = - {n \over 2},} $$ where $$n \ge 3$$ is an integer.

Answer

Solve it.
3

IIT-JEE 1997

Subjective
Prove that the values of the function $${{\sin x\cos 3x} \over {\sin 3x\cos x}}$$ do not lie between $${1 \over 3}$$ and 3 for any real $$x.$$

Answer

Solve it.
4

IIT-JEE 1996

Subjective
Find all values of $$\theta $$ in the interval $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$ satisfying the equation $$\left( {1 - \tan \,\theta } \right)\left( {1 + \tan \,\theta } \right)\,\,{\sec ^2}\theta + \,\,{2^{{{\tan }^2}\theta }} = 0.$$

Answer

$$ \pm {\pi \over 3}$$

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