If sin (alpha - beta ) = frac{1}{2} and cos ( | vedclass

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Question

(a) $\sin (\alpha - \beta ) = \frac{1}{2} = \sin 30^\circ \Rightarrow \alpha - \beta = 30^\circ $&hellip;..$(i)$

and $\cos (\alpha + \beta ) = \fra

Vedclass · Accepted Answer

$\alpha = 45^\circ ,\beta = 15^\circ $

Vedclass · Answer

(a) $\sin (\alpha - \beta ) = \frac{1}{2} = \sin 30^\circ \Rightarrow \alpha - \beta = 30^\circ $&hellip;..$(i)$

and $\cos (\alpha + \beta ) = \frac{1}{2} \Rightarrow \alpha + \beta = 60^\circ $&hellip;..$(ii)$

Solving $(i)$ and $(ii)$, we get $\alpha = 45^\circ $ and $\beta = 15^\circ $.

Trick : In such type of problems, students should satisfy the given conditions with the values given in the options.

Here $\alpha = 45^\circ $ and $\beta = 15^\circ $ satisfy both the conditions.

If $\sin (\alpha - \beta ) = \frac{1}{2}$ and $\cos (\alpha + \beta ) = \frac{1}{2},$ where $\alpha $ and $\beta $ are positive acute angles, then

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