已知:sin(兀/4+a)=1/3,且a属于(兀/4,兀),求(1)1+tana/1-tana?(2)cos(a-兀/4)+sin2a的值.
问题描述:
已知:sin(兀/4+a)=1/3,且a属于(兀/4,兀),求(1)1+tana/1-tana?(2)cos(a-兀/4)+sin2a的值.
答
a∈(π/4,π) π/4+a∈(π/2,5π/4)
cos(π/4+a)=-2√2/3
(1)(1+tana)/(1-tana)=(cosa+sina)/(cosa-sina)=sin(π/4+a)/cos(π/4+a)=-√2/4
(2)cos(a-π/4)+sin2a=sin(a+π/4)+[sin(a+π/4)cos(a-π/4)-sin(a-π/4)cos(a+π/4)]
=sin(a+π/4)+[sin(a+π/4)sin(a+π/4)-cos(a+π/4)cos(a+π/4)]=-4/9