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Separatic into real and imaginary parts of sin-1 (eio).
1 Answer
written 3.9 years ago by |
eiθ=sin(x+iy)
cosθ+isinθ=sinx cos hy+icosx sin hy
cosθ=sinx cos hy⋯Equation 1
sinx=cosθcoshy
sinθ=cosx sinhy⋯Equation 2
cosx=sinθsinhy
cos2θcosh2y+sin2θsinh2y=1
cos2θ sin h2y +sin2θ cosh2y=cosh2y×sinh2y
(1−sin2θ) sinh2y +sin2θ (1+sinh2y)=(1+sinh2y)×sinh2y$
sinh2y −sin2θ sinh2y +sin2θ +sin2θ sinh2y=sinh2y+sinh4y
sin2θ=sinh4y
sinθ=sinh2y⋯Equation 3
√sinθ=sinhy
y=sinh−1√sinθ
sin2θ=cos2x sinθ⋯From Equation 3
cos2x=sinθ
cosx=√sinθ
x=cos−1(√sinθ)