Let us show that:

cos²57° + cos²33° = 1

Given, cos²57° + cos² 33°

Need to prove the given equation as one

⇒ we know that cos(90 - θ) = sinθ

∴ cos33° = cos(90 - 57)°

= sin57° - - - eq (1)

⇒ Substitute eq(1) in the given equation

∴ cos²57° + sin²57°

⇒ we know that, sin²θ + cos²θ = 1

∴ cos²57° + sin²57° = 1

Hence, proved