\(\tan \theta \cos 60°=\cfrac{{\sqrt3}}{2}\) হলে, \(\sin (\theta-15°)\) এর মান হবে _____ ।
Madhyamik 2023
\(\tan \theta \cos 60°=\cfrac{{\sqrt3}}{2}\) হলে, \(\sin (\theta-15°)\) এর মান হবে \(\cfrac{1}{\sqrt2}\) ।
\(\tan \theta \cos 60°=\cfrac{{\sqrt3}}{2}\)
বা, \(\tan \theta \times \cfrac{1}{2}=\cfrac{{\sqrt3}}{2}\)
বা, \(\tan \theta=\cfrac{{\sqrt3}}{2} \times \cfrac{2}{1}\)
বা, \(\tan \theta=\sqrt3=\tan 60^o\)
বা, \(\theta=60^o\)
\(\therefore \sin (\theta-15°)\)
\(=\sin(60^o-15^o)\)
\(=\sin 45^o\)
\(=\cfrac{1}{\sqrt2}\) (Answer)