Question

If a+b=y and tan a / tan b = x/y then prove that sin (a-b) = {(x-y)/(x+y)}× sin y​

Answer 1

Answer:

tan a / tan b = x/y

=> (sin a / cos a) / ( sin b / cos b ) = x/y

=> (sin a cos b / cos a sin b) = x/y

By Componendo - Dividendo Rule

=> (sin a cos b + cos a sin b) / (sin a cos b - cos a sin b) = ( x + y) / ( x - y)

=> sin ( a + b) / sin ( a - b) = ( x + y) / ( x - y)

=> sin (a-b) = {(x-y)/(x+y)} sin (a+b)

=> sin (a-b) = {(x-y)/(x+y)}× sin y

Hence proof follows

Please Mark it Brainliest