Question

若tanα=-1/2,则(sinα-cosα)的平方/cos2α等于

Answer 1

（sinα-cosα)²/cos2α

=(sin²α+cos²α-2sinαcosα)/(cos²α-sin²α)

=(tan²α+1-2tanα)/(1-tan²α) （分子分母同除以cos²α)

=(1-tanα)²/(1+tanα)(1-tanα)

=(1-tanα)/(1+tanα)

=(1+1/2)/(1-1/2)

=3