Question

For any two real numbers C and D sin c-sin d =​

Answer 1

Answer:

for any real number,

$sinC - sinD = 2cos( \frac{C + D}{2} )sin( \frac{C - D}{2} )$

Proof:

as we know that

sin(A+B)- sin(A-B)=2sinAcosB...........(a)

now,

let,

A+B=C........1 and

A-B=D.........2

from eq.1+eq.2

2A=C+D

$A = \frac{C + D}{2}$

and similarly on subtracting this two eq. we get,

$B = \frac{C - D}{2}$

now, substituting this two values in eq. (a)

we get,

$sinC - sinD= 2cos( \frac{C+ D}{2} )sin( \frac{C - D}{2} )$

this is your answer hope it helps to you☺️

Answer 2

Answer:

this is the answer.. ......