已知sina=根号2cosB,tana=根号3cotB,-兀/2

已知sina=根号2cosB,tana=根号3cotB,-兀/2
已知sina=根号2cosB,tana=根号3cotB,-兀/2

已知sina=根号2cosB,tana=根号3cotB,-兀/2
∵sinα=√2cosβ ①
∴cosαtanα=√2sinβcotβ
又 tanα=√3cotβ
则 √3cosα=√2sinβ ②
由①²+②²,有
左边=(sin²α+cos²α)+2cos²α=1+2cos²α
=2(cos²β+sin²β)=2=右边
即 2cos²α=1
∴|cosα|=√2/2
而 α∈(-π/2,π/2)
∴ α=±π/4
当 α=π/4时
cosβ=sinπ/4/(√2)=1/2
而 β∈(0,π)
∴ β=π/3
同理,当α=-π/4时,可得β=2π/3

sinA = tanA cosA = tanA √(1 - (sinA)^2)
√2 cosB = √3cotB √(1 - 2(cosB)^2)
√2 sinB = √3√(1 - 2(cosB)^2)
2(1 - (cosB)^2) = 3 - 6(cosB)^2
cosB = 1/2
B = π/3
sinA = √2/2
A = π/4