三角比证明若(tanα)^2=2(tanβ)^2+1,求证(sinβ)^2=2(sinα)^2-1

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/28 15:46:20
三角比证明若(tanα)^2=2(tanβ)^2+1,求证(sinβ)^2=2(sinα)^2-1

三角比证明若(tanα)^2=2(tanβ)^2+1,求证(sinβ)^2=2(sinα)^2-1
三角比证明
若(tanα)^2=2(tanβ)^2+1,求证(sinβ)^2=2(sinα)^2-1

三角比证明若(tanα)^2=2(tanβ)^2+1,求证(sinβ)^2=2(sinα)^2-1
(tanα)^2=2(tanβ)^2+1
=2(sinb)^2/(cosb)^2+1
=[1+(sinb)^2]/(cosb)^2
=[1+(sinb)^2] / [1-(sinb)^2]
=-1+2/[1-(sinb)^2]
1-(sinb)^2=2/[1+(tana)^2]
=2/[1/(cosa)^2]
=2(cosa)^2
(sinb)^2=1-2(cosa)^2
=[2-2(cosa)^2]-1
=2(sina)^2-1