SOLUTION: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. Round your answers to three decimal places wh

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Question 888065: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list. Round your answers to three decimal places where appropriate.)
tanθ/2 − sin θ = 0
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
tan%28theta%2F2%29-sin%28theta%29%22%22=%22%22%220%22

       Use identity sin%282alpha%29=2sin%28alpha%29cos%28alpha%29
       with alpha=theta%2F2
                    sin%282%2Aexpr%28theta%2F2%29%29=2sin%28theta%2F2%29cos%28theta%2F2%29
                    sin%28theta%29=2sin%28theta%2F2%29cos%28theta%2F2%29

tan%28theta%2F2%29-sin%28theta%29%22%22=%22%22%220%22 

tan%28theta%2F2%29-2sin%28theta%2F2%29cos%28theta%2F2%29%22%22=%22%22%220%22

sin%28theta%2F2%29%2Fcos%28theta%2F2%29-2sin%28theta%2F2%29cos%28theta%2F2%29%22%22=%22%22%220%22

Multiply through by cos%28theta%2F2%29

sin%28theta%2F2%29-2sin%28theta%2F2%29cos%5E2%28theta%2F2%29%22%22=%22%22%220%22

Factor out sin%28theta%2F2%29

sin%28theta%2F2%29%281-2cos%5E2%28theta%2F2%29%29%22%22=%22%22%220%22

sin%28theta%2F2%29%22%22=%22%22%220%22;  1-2cos%5E2%28theta%2F2%29%22%22=%22%22%220%22

theta%2F2%22%22=%22%22%220%22;  -2cos%5E2%28theta%2F2%29%22%22=%22%22-1

theta%22%22=%22%22%220%22;  cos%5E2%28theta%2F2%29%22%22=%22%221%2F2
                                  
          cos%28theta%2F2%29%22%22=%22%22%22%22+%2B-+sqrt%281%2F2%29
          cos%28theta%2F2%29%22%22=%22%22%22%22+%2B-+sqrt%282%29%2F2
          theta%2F2%22%22=%22%22matrix%281%2C3%2Cpi%2F4%2C%22%2C%22%2C3pi%2F4%29
          theta%22%22=%22%22matrix%281%2C3%2Cpi%2F2%2C%22%2C%22%2C3pi%2F2%29

Edwin