设Sin(a+pai/2)=1/4,且a是锐角.求Sina,求Tan(a+pai/4)
问题描述：
设Sin(a+pai/2)=1/4,且a是锐角.求Sina,求Tan(a+pai/4)
答
Sin(a+π/2)=sin(π/2-(-a))=cos(-a)=cosa=1/4
sina=√15/4
tana=√15/15
tan(a+π/4)
=(tana+tanπ/4)(1-tanatanπ/4)
=(√15/15+1)/(1-√5/15)
=(√15+15)/(15-√15)