Question

已知tan(π/4+A)=3,则sin2A-2cos^2A的值为____

Answer 1

tan (π/4+a)

=(tanπ/4+tana)/(1-tanπ/4*tana)

=(tana+1)/(1-tana)=3

tana+1=3-3tana

tana=1/2

sin2a-2cos^2a

=sin2a-(cos2a+1)

=sin2a-coa2a-1

由万能公式

=2tana/[1+(tana)^2]-[1-(tana)^2]/[1+(tana)^2]-1

=1/(1+1/4)-(1-1/4)/(1+1/4)-1

=4/5-3/5-1

=-4/5