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Question

(sin222°+sin268°)(cos222°+cos268°)+sin263°+cos63°sin27=?
(a) 0
(b) 1
(c) 2
(d) 3

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Solution

(c) 2 We have: [sin2220+sin2680cos2220+cos268+sin2630+cos630sin270]=[sin2220+sin2(900220)cos2(900680)+cos2680+sin2630+cos630{sin(900630)}]=[sin2220+cos2220sin2680+cos2680+sin2630+cos630cos630] [sin(900θ)=cosθ and cos(900θ)=sinθ]=[11+sin2630+cos2630] [sin2θ+cos2θ=1]=1+1=2

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