Question

দেখাও যে, $cos60^\circ \cdot cos30^\circ + sin60^\circ \cdot$$ sin30^\circ = cos30^\circ$

Answer 1

Left Hand Side
$=cos60^\circ \cdot cos30^\circ + sin60^\circ \cdot sin30^\circ$

$=\frac{1}{2} \cdot \frac{\sqrt3}{2}+\frac{\sqrt3}{2} \cdot \frac{1}{2}$

$=\frac{\sqrt3}{4} + \frac{\sqrt3}{4}$

$=\frac{\sqrt3+\sqrt3}{4}$

$=\frac{2\sqrt3}{4}$

$=\frac{\sqrt3}{2}$

Right Hand Side
$=cos30^\circ$

$=\frac{\sqrt3}{2}$
 

$\therefore$ Left Hand Side = Right Hand Side

অর্থাৎ, $cos60^\circ \cdot cos30^\circ + sin60^\circ \cdot $$sin30^\circ=cos30^\circ$  ‍[Showed]