Asked by Karen
                Verify the identity cot{0-pi/2=-tan 0
            
            
        Answers
                    Answered by
            MathMate
            
    use the identities:
tan(x)=sin(x)/cos(x)
cot(x)=cos(x)/sin(x)
and
sin(π/2)=1, cos(π/2)=0
sin(0)=0, cos(0)=1
    
tan(x)=sin(x)/cos(x)
cot(x)=cos(x)/sin(x)
and
sin(π/2)=1, cos(π/2)=0
sin(0)=0, cos(0)=1
                    Answered by
            Steve
            
    I think she means θ when using 0
I'll use x to avoid copy/paste of special characters.
one way:
recall the definition of co-functions: function of complementary angle. So,
cos(x) = sin(pi/2 - x)
cot(x) = tan(pi/2 -x)
so, cot(x-pi/2) = -cot(pi/2 - x) = -tan(x)
or, use cot addition formula:
cot(x-pi/2) = (1+cotx cot pi/2)/(cot pi/2 - cot x) = (1+0)/(0-cotx) = 1/-cotx = -tanx
    
I'll use x to avoid copy/paste of special characters.
one way:
recall the definition of co-functions: function of complementary angle. So,
cos(x) = sin(pi/2 - x)
cot(x) = tan(pi/2 -x)
so, cot(x-pi/2) = -cot(pi/2 - x) = -tan(x)
or, use cot addition formula:
cot(x-pi/2) = (1+cotx cot pi/2)/(cot pi/2 - cot x) = (1+0)/(0-cotx) = 1/-cotx = -tanx
                    Answered by
            MathMate
            
    Thanks Steve, good thought!
    
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