SOLUTION: Solve the following equation given that 0° &#8804; &#952; < 360° : sin &#952; cos 2&#952; - cos 2&#952; = 0

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Question 967280: Solve the following equation given that 0° ≤ θ < 360° :
sin θ cos 2θ - cos 2θ = 0

Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!

sin%28theta%29.cos%282%2Atheta%29 - cos%282%2Atheta%29 = 0,

sin%28theta%29.cos%282%2Atheta%29 = cos%282%2Atheta%29.

Case 1.  cos%282%2Atheta%29 = 0.

           The equation is satisfied at this value of cos%282%2Atheta%29.

           Then  2%2Atheta = 90°  or  270°.

           Hence,  theta = 45°  or  135°.


Case 2.  cos%282%2Atheta%29  is not  0.

           Then you can divide both sides of the equation

           sin%28theta%29.cos%282%2Atheta%29 = cos%282%2Atheta%29.

           by  cos%282%2Atheta%29.  You will get

           sin%28theta%29 = 1.

           The solution is  theta = 90°.  It is the only solution under the given condition  0° <= theta < 360°.

Answer.  theta =  45°,  90°  or  135°.