Question

Question #dce98

Answer 1

Equation not true

Explanation:

Replace in the right side of the equation `sin^2 x` by `(1 - cos^2 x)`, then solve the quadratic equation for cos x.
`cos x - 2 = 1 - cos^2 x`
`cos^2 x + cos x - 3 = 0`
Use the new improved quadratic formula (Socratic Search)
`D = d^2 = b^2 - 4ac = 1 + 12 = 13` --> `d = +- 13`
There are 2 real roots:
`cos x = -b/(2a) +- d/(2a) = - 1/2 +- sqrt13/2 =`
Computing by calculator:
cos x = -0.5 + 1.80 = 1.30
cos x = - 0.5 - 1.80 = - 2.30
Both solutions are rejected (because -1 < x < 1). The equation is not true.