Answered

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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

Sagot :

Given the equation:

[tex]\sec ^2(x)-6\sec (x)=0[/tex]

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

[tex]\begin{gathered} \sec ^2(x)=6\sec (x) \\ \frac{\sec ^2(x)}{\sec (x)}=6 \\ \sec (x)=6 \\ \frac{1}{\sec (x)}=\frac{1}{6} \\ \cos (x)=\frac{1}{6} \\ x=\cos ^{-1}(\frac{1}{6}) \end{gathered}[/tex]

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

[tex]x=1.4033+2\pi n[/tex]

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