1-tan²α=2-1/cos^2a
1.已知tana=√2,求下列的值：①（cosa+sina）/(cosa-sina);②2sin^2-sinacosa+cos^2a....
1.已知tana=√2,求下列的值：①（cosa+sina）/(cosa-sina);②2sin^2-sinacosa+cos^2a.
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万能公式
sin2α=2tanα/(1+tan²α)=2√2/[1+(√2)²]=2√2/3
cos2α=(1-tan²α)/(1+tan²α)=[1-(√2)²]/[1+(√2)²]=-1/3
(cosα+sinα)/(cosα-sinα)
=(cosα+sinα)²/[(cosα-sinα)(cosα+sinα)]
=(sin²α+cos²α+2sinαcosα)/(cos²α-sin²α)
=(1+sin2α)/cos2α
=(1+2√2/3)/(-1/3)
=-3-2√2
2sin²α-sinαcosα+cos²α
=sin²α-sinαcosα+1
=1-cos²α-sin2α/2+1
=2-1/2-cos2α/2-sin2α/2
=3/2-[(-1/3)/2]-[(2√2/3)/2]
=5/3-√2/3
sin2α=2tanα/(1+tan²α)=2√2/[1+(√2)²]=2√2/3
cos2α=(1-tan²α)/(1+tan²α)=[1-(√2)²]/[1+(√2)²]=-1/3
(cosα+sinα)/(cosα-sinα)
=(cosα+sinα)²/[(cosα-sinα)(cosα+sinα)]
=(sin²α+cos²α+2sinαcosα)/(cos²α-sin²α)
=(1+sin2α)/cos2α
=(1+2√2/3)/(-1/3)
=-3-2√2
2sin²α-sinαcosα+cos²α
=sin²α-sinαcosα+1
=1-cos²α-sin2α/2+1
=2-1/2-cos2α/2-sin2α/2
=3/2-[(-1/3)/2]-[(2√2/3)/2]
=5/3-√2/3
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