Question

已知tanα=2,求值 (1)（cosα+sinα)/(cosα+sinα) ; (2) 2×(sinα)^2－sinα

Answer 1

(2) 2×(sinα)^2－sinαcosα＋(cosα)^2

={[ 2×(sinα)^2－sinαcosα＋(cosα)^2]/cosa^2}*cosa^2

=(2tana^2-tana+1)*cosa^2

=(8-2+1)*cosa^2

=7cosa^2

tanα=2=sina/cosa

4=sina^2/cosa^2

sina^2=4cosa^2

sina^2+cosa^2=5cosa^2=1

cosa^2=1/5

7cosa^2=7/5