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1

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 $$C$$. ## Answer $${45^ \circ },\,\,\,{60^ \circ },\,\,\,{75^ \circ }$$ 2 ### IIT-JEE 1984 Subjective Find the values of $$x \in \left( { - \pi , + \pi } \right)$$ which satisfy the equation $${g^{(1 + \left| {\cos x} \right| + \left| {{{\cos }^2}x} \right| + \left| {{{\cos }^3}x} \right| + ...)}} = {4^3}$$ ## Answer $$\pm {\pi \over 3}, \pm {{2\pi } \over 3}$$ 3 ### IIT-JEE 1983 Subjective Show that $$16\cos \left( {{{2\pi } \over {15}}} \right)\cos \left( {{{4\pi } \over {15}}} \right)\cos \left( {{{8\pi } \over {15}}} \right)\cos \left( {{{16\pi } \over {15}}} \right) = 1$$$

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4

### IIT-JEE 1983

Subjective
Find all solutions of $$4{\cos ^2}\,x\sin x - 2{\sin ^2}x = 3\sin x$$

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