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सिद्ध कीजिए कि $\frac{\sin (x+y)}{\sin (x-y)} = \frac{\tan x + \tan y}{\tan x - \tan y}$.

यदि $\sin \alpha = 1/\sqrt{5}$ और $\sin \beta = 3/5$ है,तो $\beta - \alpha$ किस अंतराल में स्थित है?

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सिद्ध कीजिए कि $\cot 4x(\sin 5x + \sin 3x) = \cot x(\sin 5x - \sin 3x)$

सिद्ध कीजिए कि $\cos 2x \cos \frac{x}{2} - \cos 3x \cos \frac{9x}{2} = \sin 5x \sin \frac{5x}{2}$

$\cos \alpha \sin (\beta-\gamma) + \cos \beta \sin (\gamma-\alpha) + \cos \gamma \sin (\alpha-\beta)$ का मान क्या है?

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