\(\tan \theta \cos 60°=\cfrac{{\sqrt3}}{2}\) 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)

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