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Mathematics
Gwendolen
17 June, 21:49
Verify sinx-siny/cosx-cosy=-cot ((x+y) / 2)
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Amy Hoover
17 June, 21:56
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Sin (A+B) = sinAcosB+cosAsinB
sin (A-B) = sinAcosB-cosAsinB
sin (A+B) - sin (A-B) = 2cosAsinB
So, if x=A+B and y=A-B, A = (x+y) / 2, B = (x-y) / 2
sinx-siny=2cosAsinB=2cos ((x+y) / 2) sin ((x-y) / 2)
cos (A+B) = cosAcosB-sinAsinB
cos (A-B) = cosAcosB+sinAsinB
cos (A+B) - cos (A-B) = - 2sinAsinB
cosx-cosy=-2sinAsinB=-2sin ((x+y) / 2) sin ((x-y) / 2).
So, (sinx-siny) / (cosx-cosy) = - cot ((x+y) / 2) QED
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