Question

Prove that : sin 54° + cos67° = sin23° + cos36°

Answer 1

Taking LHS = sin54^o + cos67^o

We know that

cos θ = sin (90° - θ)

Here, θ = 67°

⇒ sin 54°+ sin (90° - 67°)

⇒ sin 54°+ sin 23°

We also know that

Sin θ = cos (90° - θ)

Here, θ = 54°

⇒ cos (90° - 54°) + sin 23°

⇒ cos 36°+ sin 23° = RHS

Hence Proved