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) About Me  (Show Source):
You can put this solution on YOUR website!
Write cos(q) in terms of cot(q)
  
                            cot(q) = cos%28theta%29%2Fsin%28theta%29

Multiply both sides by sin(q)
                    

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


                                           Use the fact that 
                                           cosēq + sinēq = 1 
                                                   sinēq = 1 - cosēq
                                                             _________ 
                                                  sin(q) = ąÖ1 - cosēq
                        _________
               cot(q)[ąÖ1 - cosēq] = cos(q)

Square both sides:

                  cotēq[1 - cosēq] = cosēq

               cotēq - cotēq·cosēq = cosēq

                             cotēq = cosēq + cotēq·cosēq

                             cotēq = cosēq[1 + cotēq]

                           cot%5E2theta%2F%281%2Bcot%5E2theta%29 = cosēq

                        %22%22+%2B-+sqrt%28cot%5E2theta%2F%281%2Bcot%5E2theta%29%29 = cos(q)

Edwin