sin(3π - a) = sin a,cos(π/2 - b) = sin b,cos(-a)=cos a,cos(pi+b)= - cos b,
所以,有 sin a=√2 sin b,√3 cos a = - √2 cos b,
把两式平方相加,有 (sin a)^2 + 3 (cos a)^2 = 2 (sin b)^2 + 2 (cos b)^2
化简为 1 + 2 (cos a)^2 = 2,所以 cos a = √2/2
则 a 可取 π/4,或 -π/4.
当 a=π/4,sin a=√2 sin b = √2/2,√3 cos a = - √2 cos b = √6/2,
所以 sin b = 1/2,cos b = -√3/2 ,得 b = 5π/6.
当 a= - π/4,sin a=√2 sin b = -√2/2,所以 sin b = -1/2,
但当 0