Q. 195.0( 2 Votes )

Prove that :

sin 54o+cos67o= sin23o+cos36o

Answer :

Taking LHS = sin 54o+cos67o

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


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