已知tanα=2,求5(sinα)^2+3sinαcosα-2(cosα)^2的值
问题描述:
已知tanα=2,求5(sinα)^2+3sinαcosα-2(cosα)^2的值
答
5(sinα)^2+3sinαcosα-2(cosα)^2
=(cosα)^2〔5(tanα)^2+3tanα-2)
=1/(1+tanαtanα)*(5*4+3*2-2) 〔其中1+tanαtanα=secαsecα=1/(cosαcosα)〕
=1/(1+4) *24
=4.8