How do yo solve 2Cos^2(x) - 2sen(x) + 12 = 0 ?

1 Answer
Mar 5, 2018

See explanation

Explanation:

We want to solve the equation

2cos^2(x)-2sin(x)+12=0

Use cos^2(x)=1-sin^2(x)

2(1-sin^2(x))-2sin(x)+12=0

Simplify

-2sin^2(x)-2sin(x)+14=0

=>sin^2(x)+sin(x)-7=0

Let u=sin(x) and solve the quadratic equation

u^2+u-7=0

=>u=(-1+-sqrt(29))/2

=>sin(x)=(-1+-sqrt(29))/2

So the equation have no solutions within the real numbers
because -1<=sin(x)<=1, if you want complex solutions you can always take the inverse sine