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3.Trigonometrical Ratios, Functions and Identities
easy
જો $\sin (\alpha - \beta ) = \frac{1}{2}$ અને $\cos (\alpha + \beta ) = \frac{1}{2},$ કે જ્યાં $\alpha $ અને $\beta $ એ ધન લઘુકોણ હોય તો . . .
A
$\alpha = 45^\circ ,\beta = 15^\circ $
B
$\alpha = 15^\circ ,\beta = 45^\circ $
C
$\alpha = 60^\circ ,\beta = 15^\circ $
D
એકપણ નહીં.
Solution
(a) $\sin (\alpha – \beta ) = \frac{1}{2} = \sin 30^\circ \Rightarrow \alpha – \beta = 30^\circ $…..$(i)$
and $\cos (\alpha + \beta ) = \frac{1}{2} \Rightarrow \alpha + \beta = 60^\circ $…..$(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.
Standard 11
Mathematics
