Question

If cot 2 theta = tan 4 theta, where 2 theta and 4 theta are acute angles, find the value of sin 3 theta

Answer 1

cot2©=tan4©
=tan(90-2©]=tan4©
◆ 90-2©=4©
◆6©=90
◆©=15°
now,sin3©=sin45°
I.e sin3©=1√2

Answer 2

$\cot2 \alpha = \tan4 \alpha \\ \ \tan(90 - 2\alpha ) = \ \tan4 \alpha \\ 90 - 2 \alpha = 4 \alpha \\ 6 \alpha = 90 \\ \alpha = 15 \\ \\ \\ \sin3 \alpha = \sin(3 \times 15) = \ \sin45 = \frac{1}{ \sqrt{2} }$
Hope it will help you .