If sinC – sinD = x, then the value of x is

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If sinC – sinD = x, then the value of x is

1. 2sin (C + D) cos (C − D)
  2 2
2. 2cos (C + D) cos (C − D)
  2 2
3. 2cos (C + D) sin (C − D)
  2 2
4. 2sin (C + D) sin (D − C)
  2 2

Correct Option: C

sinC – sinD = 2 cos	C + D	. sin	C – D	= x
	2		2

Illustration
sin (A + B)
= sinA . cosB + cosA . sinB
sin (A – B)
= sinA . cosB – cosA . sinB
∴ sin (A + B) – sin (A – B)
= 2 cosA . sinB
Let, A + B = C ; A – B = D
∴ On adding,

A =	C + D
	2

On subtracting,

B =	C – D
	2

∴ sinC – sinD = 2 cos	C + D	.	C − D
	2		2