Question

If sin(Alpha+Betta) / sin(Alpha-Betta) = a+b/a-b then tan alpha×cot betta=​

Answer 1

Step-by-step explanation:

This is basic principle

$\frac{ \sin(\alpha + \beta )}{ \sin( \alpha - \beta ) } = \frac{a + b}{a - b} \\ using \: above \: principle \: \: \\ \frac{ \sin(\alpha + \beta) + sin(\alpha - \beta)}{ \sin(\alpha + \beta) - sin(\alpha - \beta)} = \frac{a}{b} \\ {using \: above \: transformation \: formula} \\ \frac{2 \sin( \alpha ) \cos( \beta ) }{ 2\cos( \alpha ) \sin( \beta ) } = \frac{a}{b} \\ \tan( \alpha ) \cot( \beta ) = \frac{a}{b}$

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