Question

Solve the equation on theinterval [0, 27).3(sec x)2 - 4 = 0TTX =[] [] []76 6 6[?]99

Answer 1

`x=(\pi)/(6),(11\pi)/(6),(5\pi)/(6),(7\pi)/(6)`

Explanation:

We have the following equation:

`3\cdot(\sec x)^2-4=0`

Solving for x (We use the substitution method):

`\begin{gathered} u=\sec x \\ \text{ replacing} \\ 3u^2-4=0 \\ u^2=(4)/(3) \\ u=\pm\sqrt[]{(4)/(3)}=\pm\frac{2\sqrt[]{3}}{3} \\ \text{ replacing} \\ \sec x=\pm\frac{2\sqrt[]{3}}{3} \\ x=\sec ^(-1)(\pm\frac{2\sqrt[]{3}}{3}) \\ x=(\pi)/(6),(11\pi)/(6),(5\pi)/(6),(7\pi)/(6) \end{gathered}`