# Trig Equation

1. Jun 16, 2009

### DERRAN

1. The problem statement, all variables and given/known data
Solve the Equation:

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

2. Relevant equations

3. The attempt at a solution
$$\frac{1}{cos^{2}A}$$ - $$\frac{3sinA}{cosA}$$ -5 =0

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

???

2. Jun 16, 2009

### Cyosis

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: Jun 16, 2009
3. Jun 16, 2009

### Дьявол

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

Just substitute and solve the quadratic equation.

Regards.

4. Jun 16, 2009

thanks