Question

Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians).sec^2(x) − 6 sec(x) = 0

Answer 1

Given the equation:

`\sec ^2(x)-6\sec (x)=0`

To solve this, we observe that sec(x) can not be 0. Simplifying the equation:

`\begin{gathered} \sec ^2(x)=6\sec (x) \\ (\sec ^2(x))/(\sec (x))=6 \\ \sec (x)=6 \\ (1)/(\sec (x))=(1)/(6) \\ \cos (x)=(1)/(6) \\ x=\cos ^(-1)((1)/(6)) \end{gathered}`

This is equal to (in radians), and given that the period of the cosine is 2π:

`x=1.4033+2\pi n`