已知x为锐角,sinx=3/5,则tan(x-派/4)=
问题描述：
已知x为锐角,sinx=3/5,则tan(x-派/4)=
答
由题设易知，sinx=3/5.cosx=4/5.tanx=3/4.∴tan(x-π/4)=[tanx-tan(π/4)]/[1+tanxtan(π/4)]=(tanx-1)/(1+tanx)=(-1/4)/(7/4)=-1/7.
答
sinx=3/5 cosx=4/5或者-4/5
sin(x-π/4)=sin(x)cos(π/4)-sin(π/4)cos(x)=-√2/10 或者7√2/10
cos(x-π/4)=cos(x)cos(π/4)+sin(x)sin(π/4)=7√2/10 或者-√2/10
所以tan(x-π/4)=-1/7 (cosx=4/5)
或者tan(x-π/4)=-7 (cosx=-4/5)
答
cosx=±√[1-(sinx)^2] =±4/5
∵x为锐角
∴cosx=4/5
tanx=sinx/cosx=3/4
tan[x- (π/4)] = [tanx - tan(π/4)]/[1+tanxtan(π/4)] = (tanx-1)/(1+tanx) = (-1/4)/(7/4) =-1/7