SOLUTION: Write cos theta in terms of cot theta

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Question 564106: Write cos theta in terms of cot theta
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Write cos(q) in terms of cot(q)
  
                            cot(q) = 

Multiply both sides by sin(q)
                    

                      cot(q)sin(q) = cos(q)


                                           Use the fact that 
                                           cos²q + sin²q = 1 
                                                   sin²q = 1 - cos²q
                                                             _________ 
                                                  sin(q) = ±Ö1 - cos²q
                        _________
               cot(q)[±Ö1 - cos²q] = cos(q)

Square both sides:

                  cot²q[1 - cos²q] = cos²q

               cot²q - cot²q·cos²q = cos²q

                             cot²q = cos²q + cot²q·cos²q

                             cot²q = cos²q[1 + cot²q]

                           AMP Parsing Error of [cot^2theta/(1+cot^2theta)]: Invalid function '\theta/(1+cot^2\theta)': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70.
.
 = cos²q

                        AMP Parsing Error of ["" +- sqrt(cot^2theta/(1+cot^2theta))]: Invalid function '\theta/(1+cot^2\theta))': opening bracket expected at /home/ichudov/project_locations/algebra.com/templates/Algebra/Expression.pm line 70.
.
 = cos(q)

Edwin
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