Write all positive values within the interval of 0 degrees < $\displaystyle \theta$ < 270 degrees $\displaystyle 1 - sec^{2} 2\theta - 3tan 2\theta = 0$
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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.
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?
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.
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 $\displaystyle \tan(2 \theta) [tan + 3]= 0$?
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.
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