যদি \(\alpha+\beta\)=90° ও \(\alpha:\beta\)=2:1 হয় তবে \(sin \alpha : \sin \beta\) এর মান (a) \(3:1\) (b) \(1:3\) (c) \(\sqrt3:1\) (d) \(1:\sqrt 3\)
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Answer: C
\(\alpha:\beta = 2:1 =\frac{2}{3}:\frac{1}{3}\)
\(\because \alpha+\beta=90^o\)
\(\therefore \alpha=90^o\times \cfrac{2}{3}=60^o\)
এবং \(\beta =90^o-60^o=30^o\)
\(\therefore sin\alpha: sin\beta= sin 60^o:sin 30^o\)
\(=\cfrac{\sqrt3}{2}:\cfrac{1}{2}\)
\(=\sqrt3:1\)
\(\alpha:\beta = 2:1 =\frac{2}{3}:\frac{1}{3}\)
\(\because \alpha+\beta=90^o\)
\(\therefore \alpha=90^o\times \cfrac{2}{3}=60^o\)
এবং \(\beta =90^o-60^o=30^o\)
\(\therefore sin\alpha: sin\beta= sin 60^o:sin 30^o\)
\(=\cfrac{\sqrt3}{2}:\cfrac{1}{2}\)
\(=\sqrt3:1\)