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求证sin方a+sin方β-sinasin方β+cosa方cos方β=1
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求证sin方a+sin方β-sinasin方β+cosa方cos方β=1
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答案和解析
(sinα)^2 + (sinβ)^2 - (sinα)^2 (sinβ)^2 + (cosα)^2 (cosβ)^2
=(sinα)^2 + (sinβ)^2 [1 - (sinα)^2] + (cosα)^2 (cosβ)^2
=(sinα)^2 + (sinβ)^2 (cosα)^2 + (cosα)^2 (cosβ)^2
=(sinα)^2 + (cosα)^2 [(sinβ)^2 + (cosβ)^2]
=(sinα)^2 + (cosα)^2
=1
=(sinα)^2 + (sinβ)^2 [1 - (sinα)^2] + (cosα)^2 (cosβ)^2
=(sinα)^2 + (sinβ)^2 (cosα)^2 + (cosα)^2 (cosβ)^2
=(sinα)^2 + (cosα)^2 [(sinβ)^2 + (cosβ)^2]
=(sinα)^2 + (cosα)^2
=1
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