Which identity is most appropriate for rewriting in a factorised form while finding…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Which identity is most appropriate for rewriting sin⁡(x+h)−sin⁡x\sin(x+h)-\sin x in a factorised form while finding its derivative from first principles? (a) sin⁡C+sin⁡D=2sin⁡C+D2 cos⁡C−D2\sin C+\sin D = 2\sin\dfrac{C+D}{2}\,\cos\dfrac{C-D}{2} (b) sin⁡C−sin⁡D=2sin⁡C+D2 cos⁡C−D2\sin C-\sin D = 2\sin\dfrac{C+D}{2}\,\cos\dfrac{C-D}{2} (c) sin⁡C−sin⁡D=2cos⁡C+D2 sin⁡C−D2\sin C-\sin D = 2\cos\dfrac{C+D}{2}\,\sin\dfrac{C-D}{2} (d) cos⁡C−cos⁡D=−2sin⁡C+D2 sin⁡C−D2\cos C-\cos D = -2\sin\dfrac{C+D}{2}\,\sin\dfrac{C-D}{2}

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