Solving an Equation in [-90,0]: Sec2A-3tanA-5=0

[DERRAN]

Homework Statement

Solve the Equation:

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

Homework Equations

The Attempt at a Solution

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

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

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Did I go wrong? If not I'm stuck. Please help. Thank you.

 

[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?

 

[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.

 

[DERRAN]

thanks