Consider the statements given below: 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) Choose the correct statements.

Question

Consider the statements given below: 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) Choose the correct statements. (A) I is correct (B) II is correct (C) Both I and II are correct (D) III is correct

Tardigrade Admin · Accepted Answer

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.

Q. Consider the statements given below: I. 2cosx⋅cosy=cos(x+y)−cos(x−y) II. −2sinx⋅siny=cos(x+y)−cos(x−y) III. 2sinx⋅cosy=sin(x+y)−sin(x−y) IV. 2cosx⋅siny=sin(x+y)+sin(x−y) Choose the correct statements.

I is correct

II is correct

Both I and II are correct

III is correct

As a part of identities from above, we can also show that I. 2cosxcosy=cos(x+y)+cos(x−y) II. −2sinxsiny=cos(x+y)−cos(x−y) III. 2sinxcosy=sin(x+y)+sin(x−y) IV. 2cosxsiny=sin(x+y)−sin(x−y) Hence, option is correct.

Q. 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.

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.