Let us show that:

cos² 75° - sin²15° = 0

Given, cos²75° - sin²15°

Need to prove the given equation as zero

⇒ we know that cos(90 - θ) = sinθ

∴ cos75° = cos(90 - 15)°

= sin15° - - - eq (1)

⇒ Substitute eq(1) in the given equation

∴ cos²75° - sin²15° =

sin²15° - sin²15° = 0

Hence, proved