SOLUTION: Verify the identity. cot(x-(pi/2))=-tan(x)

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Question 919115: Verify the identity.
cot(x-(pi/2))=-tan(x)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Verify the identity.
cot(x-(pi/2))=-tan(x)
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start with left side:
cot(x-π/2)=cos(x-π/2)/sin(x-π/2)
cos(x-π/2)=cosxcos(π/2)+sinxsin(π/2)=cosx*0+sinx*1=0+sinx=sinx
sin(x-π/2)=sinxcos(π/2)-cosxsin(π/2)=sinx*0-cosx*1=0-cosx=-cosx
cot(x-π/2)=cos(x-π/2)/sin(x-π/2)=sinx/-cosx=-tanx
verified: left side=right side