+0

# find all solutions of teh equation in the interval [0, 2pi)

0
122
1

2sec^2 x + tan^2 x - 3 = 0

Guest Apr 30, 2017
Sort:

#1
+4172
+3

$$2\sec^2x+\tan^2x-3=0\\~\\ 2\cdot\frac{1}{\cos^2x}+\frac{\sin^2x}{\cos^2x}-\frac{3\cos^2x}{\cos^2x}=0\\~\\ \frac{2+\sin^2x-3\cos^2x}{\cos^2x}=0\\~\\ 2+\sin^2x-3\cos^2x=0 \qquad , \, x\neq\frac{\pi}{2}+n\pi \\~\\ 2 + (1-\cos^2x)-3\cos^2x=0 \\~\\ 3 - 4\cos^2x=0 \\~\\ \cos^2x=\frac34 \\~\\ \cos x=\frac{\sqrt3}{2}$$

From looking at a unit circle, the angles within [0, 2π) that have a cosine of $$\frac{\sqrt3}{2}$$ are $$\frac{\pi}{6}$$ and $$\frac{11\pi}{6}$$

hectictar  Apr 30, 2017

### 4 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details