Question

sin c-sin D=2coos (c+d/2)×sin (c-d/2) prove that​

Answer 1

Solution:

Let, C be x + y and D be x - y

Now,

» x + y = C

» x - y = D

On solving we get,

» x = (C + D)/2 and y = (C - D)/2

Now,

=> sin C - sin D

Substitute C = x + y and D = x - y, we get

=> sin (x + y) - sin (x - y)

= sin x cos y + cos x sin y - [sin x cos y - cos x sin y]

= 2 cos x sin y

Substituting values of x and y, we get

= 2 cos (C + D)/2 sin (C - D)/2

Hence, proved.