Let us show that:

sin66° - cos24° = 0

Given, sin66° - cos24° = 0

Need to prove the given equation as zero

⇒ we know that cos(90 - θ) = sinθ

∴ cos24° = cos(90 - 66)°

= sin66° - - - eq (1)

⇒ sin66° - cos24° = 0

[substitute eq(1)]

⇒ sin66° - sin66° = 0

Hence, LHS = RHS