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1

### IIT-JEE 1980

Subjective
Given $$\alpha + \beta - \gamma = \pi ,$$ prove that
$$\,{\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = 2\sin \alpha {\mkern 1mu} \sin \beta {\mkern 1mu} \cos y$$

Solve it.
2

### IIT-JEE 1979

Subjective
(a) Draw the graph of $$y = {1 \over {\sqrt 2 }}\left( {cinx + \cos x} \right)$$ from $$x = - {\pi \over 2}$$ to $$x = {\pi \over 2}$$.

(b) If $$\cos \left( {\alpha + \beta } \right) = {4 \over 5},\,\,\sin \,\left( {\alpha - \beta } \right) = \,{5 \over {13}},$$ and $$\alpha ,\,\beta$$ lies between 0 and $${\pi \over 4}$$, find tan2$$\alpha$$.

$${56 \over {33}}$$
3

### IIT-JEE 1978

Subjective
If $$\tan \alpha = {m \over {m + 1}}\,$$ and $$\tan \beta = {2 \over {2m + 1}},$$ find the possible values of $$\left( {\alpha + \beta } \right).$$

$$n\pi + {\pi \over 4}$$

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