tan(x+π/4)=3求sinxcosx=?

问题描述:

tan(x+π/4)=3求sinxcosx=?

tan(x+π/4)=3=(tanx+tanπ/4)/(1-tanxtanπ/4)=(1+tanx)/(1-tanx)=31+tanx=3-3tanx4tanx=2tanx=1/2=sinx/cosxcosx=2sinx又sin²x+cos²x=1即5sin²x=1sin²x=1/5所以sinxcosx=2sin...