已知(tanα)∧2=2(tanβ)∧2+1,求证:(sinβ)∧2=2(sinα)2-1 求解

2025-01-31 02:48:52
推荐回答(1个)
回答1:

(tan a)^2=2(tan b)^2+1
(sina/cosa)^2=2(sinb/cosb)^2+1
1+(sina/cosa)^2=2(sinb/cosb)^2+2
1/(cosa)^2=2/(cosb)^2
(cosa)^2=(cosb)^2/2
1-(sina)^2=[1-(sinb)^2]/2
这样就有:
(sinb)^2=2*(sina)^2-1