Question #dce98

1 Answer
Nghi N.
Oct 15, 2016

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.

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