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.) cos(2θ) + sin2(θ) = 0

Algebra ->  Rational-functions -> 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.) cos(2θ) + sin2(θ) = 0      Log On


   

Question 1054639: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
cos(2θ) + sin2(θ) = 0
Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
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Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
cos(2θ) + sin2(θ) = 0
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     What is sin2%28theta%29 ?   Is it sin%5E2%28theta%29 ?

     You use so complicated terminology and are not able to write the equation in an unambiguous way?
     I see a disproportion in it.


OK, I will assume that the equation is 

cos%282theta%29+%2B+sin%5E2%28theta%29 = 0.

Use the double-angle formula  cos%282theta%29 = cos%5E2%28theta%29+-+sin%5E2%28theta%29  and replace cos%5E2%28theta%29  by  1-sin%5E2%28theta%29.

Then you will get  cos%282theta%29 = 1-2%2Asin%5E2%28theta%29.

Thus the original equation takes the form

1-2%2Asin%5E2%28theta%29 + sin%5E2%28theta%29 = 0,  or

sin%5E2%28theta%29 = 1,  or

sin%28theta%29 = +/-1.

Answer.  theta = pi%2F2+%2B+k%2Api,  k = 0, +/-1, +/-2, . . .