Question

sin(a+b) -sin(a-b) /cos(a+b) -cos (a-b) =​

Answer 1

Answer:

Cot A

Step-by-step explanation:

Explanation is there in the image..

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Answer 2

Answer:

Formula used -

sin a +sin b = 2sin (a+b)/2 cos(a-b) /2

cos a - cos b = -2sin(a+b)/2 sin(a-b) /2

apply above formula on the question.

$\frac{ \sin( \alpha + \beta ) - \sin( \alpha - \beta ) }{ \cos( \alpha + \beta ) - \cos( \alpha - \beta ) } \\ = \frac{ 2 \sin( \frac{ (\alpha + \beta ) + ( \alpha - \beta )}{2} ) \cos( \frac{( \alpha + \beta ) - ( \alpha - \beta )}{2} ) }{ - 2 \sin( \frac{( \alpha + \beta ) + ( \alpha - \beta )}{2} ) \sin( \frac{ \alpha + \beta ) - ( \alpha - \beta ) }{2} ) } \\ = \frac{\sin( \frac{ \alpha + \beta + \alpha - \beta }{2} ) \cos( \alpha + \beta - \alpha + \beta ) }{ - \sin( \frac{ \alpha + \beta + \alpha - \beta }{2} ) \sin( \frac{ \alpha + \beta - \alpha + \beta }{2} ) } \\ = \frac{ \cos( \frac{2 \beta }{2} ) }{ - \sin( \frac{2 \beta }{2} ) } \\ = - \cot( \frac{2 \beta }{2} ) \\ = - \cot( \beta )$