Question

Cos A - Cos B is equal to ​

Answer 1

Answer:

= cosA cosB − sinA sinB cos(A − B) = cosA cosB + sinA sinB sin2 A + cos2 A = 1, sin 2A = 2 sinA cosA cos 2A = 2 cos2 A − 1=1 − 2 sin2 A 2 sinA cosB = sin(A + B) + sin(A − B)

Answer 2

Answer:

Cos A - Cos B is equal to 2 sin ½ (A + B) sin ½ (B - A).

        or

Cos A - Cos B is equal to - 2 sin ½ (A + B) sin ½ (A - B).

Step-by-step explanation:

Let us assume two compound angles A and B, given as A = X + Y and B = X - Y,

⇒ Solving, we get,

X = (A + B)/2 and Y = (A - B)/2

We know,

cos(X + Y) = cos X cos Y - sin X sin Y

cos(X - Y) = cos X cos Y + sin X sin Y

cos(X + Y) - cos(X - Y) = -2 sin X sin Y

⇒ Cos A - Cos B = - 2 sin ½ (A + B) sin ½ (A - B)

⇒ Cos A - Cos B = 2 sin ½ (A + B) sin ½ (B - A)

Hence, proved.