Question

已知tanα=-1/2,则（sinα-cosα）²/cos2α=？

Answer 1

（sinα-cosα）²/cos2α
=(sin²α+cos²α-2sinαcosα)/(cos²α-sin²α) 分子分母同时除以cos²α
=(sin²α/cos²α+cos²α/cos²α-2sinαcosα/cos²α)/(cos²α/cos²α-sin²α/cos²α)
=(tan²α+1-2tanα)/(1-tan²α)
=[(-1/2)²+1-2*(-1/2)]/[1-(-1/2)²]
=[1/4+1+1]/[1-1/4]
=(9/4)/(3/4)
=3

Answer 2

原式=(cosa-sina)²/(cos²a-sin²a)
=(cosa-sina)²/(cosa+sina)(cosa-sina)
=(cosa-sina)/(cosa+sina)
上下除cosa
=(tana-1)/(tana+1)
=-3

Answer 3

原式= sinα²-2sinαcosα+cosα²
——————————
cosα²-sinα²
上下通除cosα²得
tanα²-2tanα+1
-———————
1-tanα²
=3

Answer 4

（sinα-cosα）²/cos2α
=（sinα-cosα）²/(cosα-sinα)(cosα+sinα)
=（sinα-cosα）/(cosα+sinα)
=(tanα-1)/(1+tanα)
=(-1/2-1)/(1-1/2)
= -3

Answer 5

（sinα-cosα）²/cos2α
=(sina²-2sinacosa+cosa²)/(cosa²-sina²)
除cosa²
=(tana²-2tana+1)/(1-tana²)
=(1/4+1+1)/(1-1/4)
=(9/4)/(3/4)
=3