Question
PLEASE VERIFY THE IDENTITY
cot(theta-pi/2) = -tan theta
cot(theta-pi/2) = -tan theta
Answers
Some identities:
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
sin(a-b) = sin(a)cos(b) - cos(a)sin(b)
cot(a) = 1/tan(a)
Therefore (substituting x for theta):
cos(x-pi/2) = cos(x)cos(pi/2) + sin(x)sin(pi/2)
----------------------
sin(x-pi/2) = sin(x)cos(pi/2) - cos(x)sin(pi/2)
cos(pi/2) =0
sin(pi/2) =1
So: sin(x)/-cos(x) = -tan(x)
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
sin(a-b) = sin(a)cos(b) - cos(a)sin(b)
cot(a) = 1/tan(a)
Therefore (substituting x for theta):
cos(x-pi/2) = cos(x)cos(pi/2) + sin(x)sin(pi/2)
----------------------
sin(x-pi/2) = sin(x)cos(pi/2) - cos(x)sin(pi/2)
cos(pi/2) =0
sin(pi/2) =1
So: sin(x)/-cos(x) = -tan(x)
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