Question

Consider the statements given below:
I. $ 2 \,\cos\, x \cdot \cos\, y=\cos (x+y)-\cos (x-y)$
II. $-2 \sin \,x \cdot \sin \,y=\cos (x+y)-\cos (x-y)$
III. $2 \sin \,x \cdot \cos \,y=\sin (x+y)-\sin (x-y)$
IV. $2 \cos \,x \cdot \sin \,y=\sin (x+y)+\sin (x-y)$
Choose the correct statements.

• A. I is correct
• B. II is correct
• C. Both I and II are correct
• D. III is correct

Answer 1

Answer: (B)

As a part of identities from above, we can also show that
I. $2 \cos x \cos y=\cos (x+y)+\cos (x-y)$
II. $-2 \sin x \sin y=\cos (x+y)-\cos (x-y)$
III. $2 \sin x \cos y=\sin (x+y)+\sin (x-y)$
IV. $2 \cos x \sin y=\sin (x+y)-\sin (x-y)$
Hence, option is correct.