Question

দেখাও যে, $sin2A = \frac{2tanA}{1+tan^2A}$ যদি $A=45^\circ$ হয়।

Answer 1

দেওয়া আছে,
$A=45^\circ$

Left Hand Side
$=sin2A$

$=sin\left(2 \times 45^\circ\right)$

$=sin90^\circ$

$=1$

Right Hand Side
$= \frac{2tanA}{1+tan^2A}$

$= \frac{2tan45^\circ}{1+tan^245^\circ}$

$= \frac{2 \times 1}{1+(1)^2}$

$= \frac{2}{2}$

$= 1$

$\therefore$ Left Hand Side = Right Hand Side

অর্থাৎ $sin2A= \frac{2tanA}{1+tan^2A}$