Question

Tan(a+b)/tan(a-b)=sin2a+sin2b/sin2a-sin2b

Answer 1

Step-by-step explanation:

$use \: the \: formula \: \sin(2 \alpha ) + \sin( 2\beta ) = 2 \sin( \alpha + \beta ) \cos( \alpha - \beta ) \\ now \: rhs \: of \: the \: given \: equation \: is \: \frac{ \sin(2 \alpha ) + \sin(2 \beta ) }{\sin(2 \alpha ) - \sin(2 \beta )} \\ = \frac{2 \sin( \alpha + \beta ) \cos( \alpha - \beta ) }{2 \cos( \alpha + \beta ) \sin( \alpha - \beta ) } \\ = \frac{ \tan( \alpha + \beta ) }{ \tan( \alpha - \beta ) }$