Question

দেখাও যে, $cos^230^\circ-sin^230^\circ=cos60^\circ$

Answer 1

Left Hand Side
$=cos^230^\circ-sin^230^\circ$

$=\left(\frac{\sqrt3}{2}\right)^2-\left(\frac12\right)^2$

$=\frac34-\frac14$

$=\frac{3-1}4$

$=\frac24$

$=\frac12$

Right Hand Sid
$=cos60^\circ$

$=\frac12$

$\therefore$ Left Hand Side = Right Hand Side

অর্থাৎ, $cos^230^\circ-sin^230^\circ=cos60^\circ$  ‍[Showed]