Answer:
1 - cos² 15° - cos² 75° can be simplified as follows:
Using the identity cos² x = 1 - sin² x, we can write the expression as:
1 - (1 - sin² 15°) - (1 - sin² 75°)
= sin² 15° + sin² 75° - 1
Using the identity sin 2x = 2sin x cos x, we can write sin 15° and sin 75° in terms of sin 30° and sin 45°:
sin 15° = sin (30° - 15°) = (1/2) * sin 30°
sin 75° = sin (45° + 30°) = sin 45° + sin 30°
Substituting these values in the above expression, we get:
sin² 15° + sin² 75° = (1/4) * sin² 30° + sin² 45° + sin 30° * sin 45°
= (1/4) * (2 * (1/2)²) + (2 * (1/2) * (1/2)) + (1/2) * (1/2)
= (1/4) + 1/2 + 1/4 = 1
So, 1 - cos² 15° - cos² 75° = sin² 15° + sin² 75° - 1 = 1 - 1 = 0.
Explanation: