Question

If sin(α+β)=nsin(α-β) and n unequal to minus1 prove that cotα=n-1/n+1cotβ..
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Answer 1

Understanding:

1)If a, b, c, b are four real numbers such that

$\frac{a}{b} = \frac{c}{d}$
Then, we can say
By Componendo and dividendo,
or adding 1 , and subtracting 1 . Then on dividing, we get

$\frac{a + b}{a - b} = \frac{c + d}{c - d}$
We will use this in :-
$\frac{ \sin( \alpha + \beta ) }{ \sin( \alpha - \beta ) } = \frac{n}{1}$

For Calculation see pic,