Question

দেখাও যে, $sin60^\circ \cdot cos30^\circ + cos60^\circ \cdot $$sin30^\circ = sin90^\circ$

Answer 1

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

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

$=\frac{3}{4}+\frac{1}{4}$

$=\frac{3+1}{4}$

$=\frac{4}{4}$

$=1$

Right Hand Side
$= sin90^\circ$

$=1$

$\therefore$ Left Hand Side = Right Hand Side

অর্থাৎ, $sin60^\circ \cdot cos30^\circ + cos60^\circ \cdot $$sin30^\circ=sin90^\circ$  ‍[Showed]