Posted by **Yadira** on Wednesday, May 23, 2012 at 11:50pm.

Use factoring, the quadratic formula, or identities to solve cos(x)+1=sin^(2)x. Find all solutions on the interval [0, 2pi)

- Pre-Calc/Math -
**Jai**, Thursday, May 24, 2012 at 12:05am
recall that

sin^2 x + cos^2 x = 1

therefore, we use this substitute the sin^2 x at the right side of equation:

cos(x) + 1 = 1 - cos^2 x

cos(x) = -cos^2 x

cos(x) + cos^2 (x) = 0

factoring,

cos(x) [1 + cos(x)] = 0

*for cos(x) = 0, the x values allowed are π/2 and 3π/2.

*for (1 + cos(x)) = 0 or cos(x) = -1, the x value allowed is π.

therefore,

x = π/2, π, 3π/2

hope this helps~ :)

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