Question

The value of cos²15° - cos²30° + cos²45° - cos²60° + cos²75° is ______.

Options

• 1/4

• 2

• 1/2

• 0

Answer 1

The value of cos²15° − cos²30° + cos²45° − cos²60° + cos²75° is 1/2.

Explanation:

`cos^2 15° - cos^2 30° + cos^2 45° - cos^2 60° + cos^2 75°`

= `sin^2 75° + cos^2 75° + cos^2 45° - cos^2 60° + cos^2 30°`

= `1 + (1/sqrt2)^2 - (1/2)^2 - (sqrt3/2)^2`

= `1/2`