1.

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

Answer»

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

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