Question

please help me with q-28(i)​

Answer 1

$\frac{ \sin( \alpha ) + \sin( \beta ) }{ \cos( \alpha ) + \cos( \beta ) } = \frac{a}{b}$

$2 sin( \frac{ \alpha + \beta }{2} ) \cos( \frac{ \alpha - \beta }{2}{ )} \div 2 \cos( \frac{ \alpha + \beta }{2} ) \cos( \frac{ \alpha - \beta }{2} ) = \frac{a}{b}$

$\tan( \frac{ \alpha + \beta }{2} ) = \frac{a}{b}$

$\sin( \alpha + \beta ) = \frac{2 \tan( \frac{ \alpha + \beta }{2} ) }{1 + \tan {}^{2} ( \frac{ \alpha + \beta }{2}^{} ) {}^{} }$

$= \frac{2 \times \frac{a}{b} }{1 +( \frac{ {a}^{} }{b} {)}^{2} } = \frac{2ab}{ {b }^{2} + {a}^{2} }$

Answer 2

solution is in the pic