Trigonometry

Given the equation 2cos^2x+sinx-1=0

1. Explain why this equation cannot be factored.

2. Use a trigonometric identity to change the equation into one that can be factored.

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  1. can't be factored because different functions are involved.

    As if you had y^2+x-1 = 0

    But, using a well-known identity connecting sin and cos,

    2cos^2 + sin - 1 = 0
    2 - 2sin^2 + sin - 1 = 0
    2sin^2 - sin - 1 = 0
    (2sinx+1)(sinx-1) = 0

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