# Trig Equation

## Homework Statement

Solve the Equation:

sec2A - 3tanA - 5=0, for A $$\in$$[-90,0]

## The Attempt at a Solution

$$\frac{1}{cos^{2}A}$$ - $$\frac{3sinA}{cosA}$$ -5 =0

$$\frac{1-3sinA.cosA}{cos^{2}A}$$ -5 = 0

???

Cyosis
Homework Helper
You didn't go wrong, but the form you wrote it in only makes it harder. I suggest you write the $\sec^2 A$ term in terms of the tangent. Do you know how?

Last edited:
$$sec^2A=\frac{1}{cos^2A}=\frac{sin^2A+cos^2A}{cos^2A}=\frac{sin^2A}{cos^2A}+\frac{cos^2A}{cos^2A}=tan^2A+1$$

Just substitute and solve the quadratic equation.

Regards.

thanks