Question

if tan A = mtanB, prove that sin(A-B)/sin(A+B) =m-1/m+1​

Answer 1

tan A = m.tan B

tan A/ tan B = m

sin A . cos B / cos A . sin B m

Use componendo or dividendo rule

( sin A . cos B + cos A . sin B )

( sin A . cos B - cos A . sin B ) = ( m + 1 ) / ( m - 1 )

[ use sin ( A - B ) = sin A . cos B - cos A . sin B

sin ( A+ B ) = sin A . cos B + cos A . sin B ]

sin ( A+ B ) / sin (A- B ) = (m +1) / (m- 1 )

Hence :

sin ( A - B ) / sin ( A + B ) = ( m + 1 ) / ( m - 1 )