Given A = 60^ and B = 30^ ,prove that : (A - B) = A B + A B - Vidyadip

Question

Given $A = 60^\circ $ and $B = 30^\circ ,$prove that : $\cos (A - B) = \cos A \cos B + \sin A \sin B$

✓

Answer

Given $A = 60^\circ $ and $B = 30^\circ $
$\text{LHS} = \cos(A – B)$
$= \cos (60^\circ – 30^\circ )$
$= \cos 30^\circ $
$=\frac{\sqrt{3}}{2}$
$\text{RHS} = \cos A \cos B + \sin A \sin B$
$= \cos 60^\circ \cos 30^\circ + \sin 60^\circ \sin 30^\circ $
$=\frac{1}{2} \frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2} \frac{1}{2}$
$=\frac{\sqrt{3}}{4}+\frac{\sqrt{3}}{4}$
$=\frac{\sqrt{3}}{2}$
$\text { LHS }=\text { RHS }$

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