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Question

Evaluate : sin263+sin227cos217+cos273.

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Solution

Given
sin263+sin227cos217+cos273

[we know that 63+27=90]

Hence 63=9027

similarly 17+73=90

Hence 17=9073]

=sin2(9027)+sin227cos2(9073)+cos273

[cos(90θ)=sinθ;sin(90θ)=cosθ]

=cos227+sin227sin273+cos273

[sin2A+cos2A=1]]

=11

=1.

sin263+cos227cos77+cos273=1

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