Verify:
$sin (A - B) = sin A cos B + cos A sin B$

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Solution

$\begin{matrix} L . H . S = sin (a - b) l e t a s s u m e, a = 60^{\circ} a n d b = 30^{\circ} S o, sin (a - b) = sin (60^{\circ} - 30^{\circ}) = sin 30^{\circ} = \frac{1}{2} R . H . S = sin a \times cos b - cos a \times sin b = sin 60^{\circ} \times cos 30^{\circ} - cos 60^{\circ} \times sin 30^{\circ} = \frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} - \frac{1}{2} \times \frac{1}{2} = \frac{3}{4} - \frac{1}{4} = \frac{3 - 1}{4} = \frac{1}{2} ∴ L . H . S . = R . H . S H e n c e p r o v e d \end{matrix}$

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