Question

((2cos A + 1) + (2cos A - 1)(2cos 2A - 1) = 2cos 4A + 1)

a. True

b. False

Answer 1

The equation ((2cos A + 1) + (2cos A - 1)(2cos 2A - 1) = 2cos 4A + 1) is false.

Step-by-step explanation:

To determine whether the equation ((2cos A + 1) + (2cos A - 1)(2cos 2A - 1) = 2cos 4A + 1) is true or false, we can simplify both sides of the equation and compare them.

Starting with the left side:

(2cos A + 1) + (2cos A - 1)(2cos 2A - 1) =

2cos A + 1 + 2(cos A)(cos 2A) - (2cos A - 1) =

2cos A + 1 + 2(cos A)(cos 2A) - 2cos A + 1 =

2(cos A)(cos 2A) + 2 =

2[cos A(cos 2A + 1)] + 2 =

2cos 4A + 2

Now, we simplify the right side:

2cos 4A + 1

Since the right side is 2cos 4A + 1 and the left side is 2cos 4A + 2, the equation ((2cos A + 1) + (2cos A - 1)(2cos 2A - 1) = 2cos 4A + 1) is false.