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Question

Prove that (sin 32° cos 58° + cos 32° sin 58°) = 1.

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Solution

(sin 32° cos 58° + cos 32° sin 58°) = 1

LHS=sin320cos580+cos320sin580=sin(900580)cos580+cos(900580)sin580=cos580×cos580+sin580×sin580 [sin(900θ)=cosθ,cos(900θ)=cosθ] =cos2580+sin2580=1 [sin2θ+cos2θ=1]=RHS

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