How to prove cos(pi - theta)+sin(pi/2 + theta)=0
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How to prove cos(pi - theta)+sin(pi/2 + theta)=0

[From: ] [author: ] [Date: 12-08-27] [Hit: ]
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cos(π - x) + sin(π/2 + x) =
cos π cos x + sin π sin x + sin π/2 cos x + sin x cos π/2 =
∙ ∙ ∙ -1 • cos x + 0 • sin x + 1 • cos x + sin x • 0 =
∙ ∙ ∙ ∙ ∙ ∙ – cos x ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ + cos x =
∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 0

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Since cos(π - θ) = -cos(θ) and sin(π/2 + θ) = sin(π/2 - (-θ)) = cos(-θ) = cos(θ),

cos(π - θ) + sin(π/2 + θ) = -cos(θ) + cos(θ) = 0.
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