Question

cos 2A + 2 cos A is always​

Answer 1

Given: cos 2A + 2 cos A

To find: The given trigonometric term is?

Solution:

• Now the  trigonometric term given is cos 2A + 2 cos A.

• We know the formula of cos 2A as:

                cos 2A = 2 cos^2 A - 1

• So putting it in given term, we get:

                = 2 cos^2 A - 1 + 2 cos A

                = 2 ( cos A + 1/2 )^2 - 3/2

• Now  ( cos A + 1/2 )^2 ≥ 0 for all A

• Adding -3/2 to it, we get:

                ( cos A + 1/2 )^2 - 3/2 ≥ -3/2 for all A

• So, cos 2A + 2 cos A ≥ -3/2 for all A

Answer:

            So, the given trigonometric term cos 2A + 2 cos A is always greater than -3/2.