The value π/12 is a solution to the equation 2 cos² (4x) - 1 = 0. True or false?

An equation involving trigonometric ratios of an angle is called a trigonometric identity.

Answer: False

We will use trigonometric identity to solve this question.

Explanation:

2cos²(4x) - 1 = cos(8x) 

Substitute π/12 for x in the above equation.

cos(8 × π/12) = cos(2π/3)

= cos(π - π/3)

= - cos(π/3)

= - 1/2

This is not equal to 0.

Thus, the value π/12 is not a solution to the equation 2 cos² (4x) - 1 = 0. The statement is false.