1. Solve for theta

Write all positive values within the interval of 0 degrees < $\displaystyle \theta$ < 270 degrees

$\displaystyle 1 - sec^{2} 2\theta - 3tan 2\theta = 0$

2. Originally Posted by reiward
Write all positive values within the interval of 0 degrees < $\displaystyle \theta$ < 270 degrees

$\displaystyle 1 - sec^{2} 2\theta - 3tan 2\theta = 0$
Substitute $\displaystyle \sec^2 (2 \theta) = \tan^2 (2 \theta) + 1$, simplify and solve the resulting simple trig equation.

3. Originally Posted by mr fantastic
Substitute $\displaystyle \sec^2 (2 \theta) = \tan^2 (2 \theta) + 1$, simplify and solve the resulting simple trig equation.
$\displaystyle 1 - sec^{2} 2\theta - 3tan 2\theta = 0$

$\displaystyle 1 - (\tan^2 (2 \theta) + 1) - 3tan 2\theta = 0$

$\displaystyle \tan^2 (2 \theta) - 3tan 2\theta = 0$

Im stuck. What do I factor it to?

4. Originally Posted by reiward
$\displaystyle 1 - sec^{2} 2\theta - 3tan 2\theta = 0$

$\displaystyle 1 - (\tan^2 (2 \theta) + 1) - 3tan 2\theta = 0$

$\displaystyle \tan^2 (2 \theta) - 3tan 2\theta = 0$ Mr F says: This is wrong. There is a careless mistake in signs.

Im stuck. What do I factor it to?
Factorise. Note that $\displaystyle \tan (2 \theta)$ is a common factor. Then use the Null Factor Law to get two simple trig equations. Solve them.

5. Originally Posted by mr fantastic
Substitute $\displaystyle \sec^2 (2 \theta) = \tan^2 (2 \theta) + 1$, simplify and solve the resulting simple trig equation.
Originally Posted by mr fantastic
Factorise. Note that $\displaystyle \tan (2 \theta)$ is a common factor. Then use the Null Factor Law to get two simple trig equations. Solve them.
Oh okay.

$\displaystyle -\tan^2 (2 \theta) - 3tan 2\theta = 0$

Can I make that to $\displaystyle \tan^2 (2 \theta) + 3tan 2\theta = 0$ ?

If so, would the factor be $\displaystyle \tan(2 \theta) [tan + 3]= 0$?

6. Originally Posted by reiward
Oh okay.

$\displaystyle -\tan^2 (2 \theta) - 3tan 2\theta = 0$

Can I make that to $\displaystyle \tan^2 (2 \theta) + 3tan 2\theta = 0$ ?

If so, would the factor be $\displaystyle \tan(2 \theta) [tan + 3]= 0$?
Yes.
Yes.