cos(α+π/4)+sin2α 怎么化简
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cos(α+π/4)+sin2α 怎么化简
cos(α+π/4)+sin2α 怎么化简
cos(α+π/4)+sin2α 怎么化简
无法再化简
cos(α+π/4)+sin2α
=cosαcosπ/4-sinαsinπ/4+2sinαcosα
=√2/2(cosα-sinα)+2sinαcosα
cos(α+π/4)+sin2α
=cosαcosπ/4-sinαsinπ/4+2sinαcosα
=√2/2(cosα-sinα)+2sinαcosα
(cosα-sinα)^2=1-2sinαcosα
2sinαcosα=1-(cosα-sinα)^2
cos(α+π/4)+sin2α=√2/2(cosα-sinα)+2sinαcosα
...
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cos(α+π/4)+sin2α
=cosαcosπ/4-sinαsinπ/4+2sinαcosα
=√2/2(cosα-sinα)+2sinαcosα
(cosα-sinα)^2=1-2sinαcosα
2sinαcosα=1-(cosα-sinα)^2
cos(α+π/4)+sin2α=√2/2(cosα-sinα)+2sinαcosα
=√2/2(cosα-sinα)+1-(cosα-sinα)^2
=-2cos^2(α+π/4)+cos(α+π/4)+1
收起
=√2/2(cosα-sinα)+2sinαcosα
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