Question

prove geometrically that cos (A+B) = cos A Cos B - sin A Sin B and hence prove that cos2A = cos square A - sin square A​

Answer 1

Step-by-step explanation:

How to prove cos (A+B) = cos A cos B - sin A sin B?

Consider a right angle triangle ABC such that AC =3 cm, BC = 4 cm and AB = 5 cm, here <ACB is the right angle. So <A + <B = 180 -<C = 90 deg.

sin A = 4/5; cos A = 3/5; sin B = 3/5 and cos B = 4/5.

cos (A+B) = cos A cos B - sin A sin B

Here RHS = cos A cos B - sin A sin B

= (3/5)(4/5) - (4/5)(3/5) = 1–1 = 0 which is the same as cos (A+B) or cos 90 which is 0.

Hence, cos (A+B) = cos A cos B - sin A sin B.