1

### IIT-JEE 1992

Subjective
Show that the value of $${{\tan x} \over {\tan 3x}},$$ wherever defined never lies between $${1 \over 3}$$ and 3.

Solve it.
2

### IIT-JEE 1991

Subjective
If $$\exp \,\,\,\left\{ {\left( {\left( {{{\sin }^2}x + {{\sin }^4}x + {{\sin }^6}x + \,\,\,..............\infty } \right)\,In\,\,2} \right)} \right\}$$ satiesfies the equation $${x^2} - 9x + 8 = 0,$$ find the value of $${{\cos x} \over {\cos x + \sin x}},\,0 < x < {\pi \over 2}.$$

$${{\sqrt 3 - 1} \over 2}$$
3

### IIT-JEE 1990

Subjective
$$ABC$$ is a triangle such that $$\sin \left( {2A + B} \right) = \sin \left( {C - A} \right) = \, - \sin \left( {B + 2C} \right) = {1 \over 2}.$$\$

If $$A,\,B$$ and $$C$$ are in arithmetic progression, determine the values of $$A,\,B$$ and $$C$$.

$${45^ \circ },\,\,\,{60^ \circ },\,\,\,{75^ \circ }$$
4

### IIT-JEE 1984

Subjective
Find the values of $$x \in \left( { - \pi , + \pi } \right)$$ which satisfy the equation $${g^{(1 + \left| {\cos x} \right| + \left| {{{\cos }^2}x} \right| + \left| {{{\cos }^3}x} \right| + ...)}} = {4^3}$$

$$\pm {\pi \over 3}, \pm {{2\pi } \over 3}$$

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NEET

Class 12