Question

已知(1+tanx)/(1-tanx)=2 求cos^2(π+x)+3sin(π-x)cos(-x)+2sin^2(2π

Answer 1

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

1+tanx=2-2tanx

tanx=1/3

cosx^2=1/(1+tanx^2)=1/(10/9)=9/10

cosx^2+3sinxcosx+2sinx^2=1+3tanxcosx^2+(1-cosx^2)=1+3*(1/3)*(9/10)+(1-9/10)=2