Mathc initiation/a78a
| Trigonométriques |
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cos(x)^2 + sin(x)^2 = 1
cosh(x)^2 - sinh(x)^2 = 1
sec(x)^2 - tan(x)^2 = 1
sech(x)^2 + tanh(x)^2 = 1
csc(x)^2 - cot(x)^2 = 1
coth(x)^2 - csch(x)^2 = 1
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sin(x+y) = cos(x) sin(y) + sin(x) cos(y)
sinh(x+y) = cosh(x) sinh(y) + sinh(x) cosh(y)
cos(x+y) = cos(x) cos(y) - sin(x) sin(y)
cosh(x+y) = cosh(x) cosh(y) + sinh(x) sinh(y)
sin(x-y) = sin(x) cos(y) - cos(x) sin(y)
sinh(x-y) = sinh(x) cosh(y) - cosh(x) sinh(y)
cos(x-y) = cos(x) cos(y) + sin(x) sin(y)
cosh(x-y) = cosh(x) cosh(y) - sinh(x) sinh(y)
tan(x+y) = (tan(x)+ tan(y))/(1- tan(x) tan(y))
tanh(x+y) = [tanh(x)+tanh(y)]/[1+tanh(x) tanh(y)]
tan(x-y) = [ tan(x)- tan(y)]/[1+ tan(x)* tan(y)]
tanh(x-y) = [tanh(x)-tanh(y)]/[1-tanh(x)*tanh(y)]
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cos(2x) = cos(x)^2 - sin(x)^2
= 1 - 2sin(x)^2
= 2cos(x)^2 - 1
cosh(2x) = cosh(x)^2 + sinh(x)^2
= 1 + 2sinh(x)^2
= 2cosh(x)^2 - 1
cos(3x) = 4cos(x)^3 - 3cos(x)
cosh(3x) = 4cosh(x)^3 - 3cosh(x)
cos(4x) = 8cos(x)^4 - 8cos(x)^2 + 1
cosh(4x) = 8cosh(x)^4 - 8cosh(x)^2 + 1
sin(2x) = 2cos(x) sin(x)
sinh(2x) = 2cosh(x) sinh(x)
sin(3x) = 3sin(x) - 4sin(x)^3
sinh(3x) = 3sinh(x) + 4sinh(x)^3
sin(4x) = 4sin(x) cos(x) - 8sin(x)^3 cos(x)
sinh(4x) = 4cosh(x) sinh(x) + 8sinh(x)^3 cosh(x)
tan(2x) = (2 tan(x))/(1 - tan(x)^2)
tanh(2x) = (2tanh(x))/(1 + tanh(x)^2)
tan(3x) = (3tan(x)- tan(x)^3)/(1- 3tan(x)^2)
tanh(3x) = (3tanh(x)+tanh(x)^3)/(1+3tanh(x)^2)
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cos(x)^2 = 1/2 + 1/2 cos(2x)
cosh(x)^2 = 1/2 + 1/2 cosh(2x)
cos(x)^3 = 3/4 cos(x) + 1/4 cos(3x)
cosh(x)^3 = 3/4 cosh(x) + 1/4 cosh(3x)
cos(x)^4 = 3/8 + 1/2 cos(2x) + 1/8 cos(4x)
cosh(x)^4 = 3/8 + 1/2 cosh(2x) + 1/8 cosh(4x)
sin(x)^2 = 1/2 - 1/2 cos(2x)
sinh(x)^2 = 1/2 cosh(2x) - 1/2
sin(x)^3 = 3/4 sin(x) - 1/4 sin(3x)
sinh(x)^3 = 1/4 sinh(3x) - 3/4 sinh(x)
sin(x)^4 = 3/8 - 1/2 cos(2x) + 1/8 cos(4x)
sinh(x)^4 = 3/8 - 1/2 cosh(2x) + 1/8 cosh(4x)
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sin(x/2) = sqrt( (1-cos(x))/2)
cos(x/2) = sqrt( (1+cos(x))/2)
tan(x/2) = sqrt( (1-cos(x))/(1+cos(x)) )
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sin(x) sin(y) = 1/2 [ cos(x-y) - cos(x+y)]
sinh(x)sinh(y) = 1/2 [cosh(x+y) - cosh(x-y)]
cos(x) cos(y) = 1/2 [ cos(x-y) + cos(x+y)]
cosh(x)cosh(y) = 1/2 [cosh(x-y) + cosh(x+y)]
sin(x) cos(y) = 1/2 [ sin(x-y) + sin(x+y)]
sinh(x)cosh(y) = 1/2 [sinh(x-y) + sinh(x+y)]
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sin(x) + sin(y) = 2sin((x+y)/2) cos((x-y)/2)
sinh(x) + sinh(y) = 2sinh((x+y)/2) cosh((x-y)/2)
sin(x) - sin(y) = 2sin((x-y)/2) cos((x+y)/2)
sinh(x) - sinh(y) = 2sinh((x-y)/2) cosh((x+y)/2)
cos(x) + cos(y) = 2cos((x+y)/2) cos((x-y)/2)
cosh(x) + cosh(y) = 2cosh((x+y)/2) cosh((x-y)/2)
cos(x) - cos(y) = -2sin((x+y)/2) sin((x-y)/2)
= 2sin((x+y)/2) sin((y-x)/2)
cosh(x) - cosh(y) = 2sinh((x+y)/2) sinh((x-y)/2)
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sin( acos(x)) = sqrt(1-x^2)
sinh(acosh(x)) = sqrt(x^2 - 1)
cos( asin(x)) = sqrt(1-x^2)
cosh(asinh(x)) = sqrt(x^2 + 1)
sec(atan(x)) = sqrt(1+x^2)
csc(acot(x)) = sqrt(1+x^2)
tan( asec(x)) = sqrt(x^2-1)
tanh(asech(x)) = sqrt(1 - x^2)
cot( acsc(x)) = sqrt(x^2-1)
coth(acsch(x)) = sqrt(1 + x^2)
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