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13 lines
641 B
Plaintext
13 lines
641 B
Plaintext
; Mathomatic fails to completely simplify the following 3 identities with the simplify command.
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; Solving for x or 0 verifies they are identities.
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; (cos(4x)+cos(3x)+cos(2x))/(sin(4x)+sin(3x)+sin(2x))=cot(3x)
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((((e^(4*i*x)) + (e^(-4*i*x)))/2) + (((e^(3*i*x)) + (e^(-3*i*x)))/2) + (((e^(2*i*x)) + (e^(-2*i*x)))/2))/((((e^(4*i*x)) - (e^(-4*i*x)))/(2*i)) + (((e^(3*i*x)) - (e^(-3*i*x)))/(2*i)) + (((e^(2*i*x)) - (e^(-2*i*x)))/(2*i))) = i*((e^(3*i*x)) + (e^(-3*i*x)))/((e^(3*i*x)) - (e^(-3*i*x)))
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((e^x) - 1)/((e^(x/2)) + 1) = (e^(x/2)) - 1
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((4^x) - 1)/((4^(x/2)) + 1) = (4^(x/2)) - 1
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simplify all
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copy all
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:solve 1-3 x
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solve 4-6 verifiable 0
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