Q. 183.7( 3 Votes )

Prove that :

sin2 25o+sin2 65° = cos2 63°+cos2 39o

Answer :

Taking LHS = sin 25o+sin65o

We know that


Sin θ = cos (90° - θ)


Here, θ = 25°


cos2 (90° - 25°)+ sin2 65°


cos2 65° + sin2 65°


= 1 [ cos2 θ + sin2 θ = 1]


Now, RHS = cos2 63o+cos2 39o


We know that


cos θ = sin (90° - θ)


Here, θ = 39°


cos2 63° + sin2 (90° - 39°)


cos2 63°+ sin2 63°


=1 [ cos2 θ + sin2 θ = 1]


LHS = RHS


Hence Proved


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