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.

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
1079 views around the world
You can reuse this answer
Creative Commons License