Question

দেখাও যে, $cos3A=4cos^3A-3cosA$ যদি $A=30^\circ$ হয়।

Answer 1

দেওয়া আছে,
$A=30^\circ$

Left Hand Side
$=cos3A$

$=cos(3 \times 30^\circ)$

$=cos90^\circ$

$=0$

Right Hand Side
$=4cos^3A-3cosA$

$=4cos^330^\circ-3cos30^\circ$

$=4\left(\frac{\sqrt3}{2}\right)^3 - 3 \times \frac{\sqrt3}{2}$

$=\left(4 \times \frac{3\sqrt3}{8}\right) - \left(3 \times \frac{\sqrt3}{2}\right)$

$=\frac{3\sqrt3}{2} - \frac{3\sqrt3}{2}$

$=0$

$\therefore$ Left Hand Side = Right Hand Side

অর্থাৎ $cos3A=4cos^3A-3cosA$ [দেখানো হলো]