Question

If tan (alpha)= n . tan(beta) and sin(alpha)= m . sin (beta) prove that sin(alpha)=(√n^2-m^2)/(n^2-1)

Answer 1

Step-by-step explanation:

$\tan( \alpha ) = n \tan( \beta )$

$\sin( \alpha ) = m \sin( \beta )$

$\frac{ \sin( \alpha ) }{ \ \cos ( \ \alpha ) } = n \times \frac{ \sin( \beta ) }{ \cos( \beta ) }$

$\frac{m \sin( \beta ) }{ \cos( \alpha ) } = n \times \frac{ \sin( \beta ) }{ \cos( \beta ) }$

$\frac{ \cos( \alpha ) }{ \cos( \beta ) } = \frac{n}{m}$

then using this expansion find given