How do you solve 4cos^2x-5sinxcosx-6=0?

1 Answer
Dec 3, 2015

solve trig equation.

Explanation:

4cos^2 x - 5sin x.cos x - 6 = 0
Try to transform the equation into a linear function in sin 2x and
cos 2x. Replace 4cos^2 x = 2(1 + cos 2x) and
5sin x.cos x by 5/2sin 2x.
2 + 2cos 2x - (5/2)sin 2x - 6 = 0
2cos2x - 5/2sin 2x - 4 = 0
cos 2x - (5/4)sin 2x = 2
Calltan a = sin a/(cos a) = 5/4 --> a = 51^@34 --> cos a = 0.62
cos 2x.cos a - sin a.sin 2x = 2cos a
cos (2x + 51.34) = 2(0.62) = 1.25 > 1.
This trig equation is insolvable since any cos must be < 1.
The number 6 should be 5 or less in order to make the equation solvable.