Find all solutions of the equation in the interval $[0,2 \pi)$.
\[
\sec \theta-1=0
\]

Answer

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Answer

Final Answer: The solution to the equation $\sec \theta-1=0$ in the interval [0,2 \pi) is $\boxed{0}$

Steps

Step 1 ：Rewrite the given equation $\sec \theta-1=0$ as $\frac{1}{\cos \theta} - 1 = 0$

Step 2 ：Solve the equation for $\cos \theta$ to get $\cos \theta = 1$

Step 3 ：The solutions to this equation in the interval [0, 2π) are $\theta = 0$ and $\theta = 2\pi$

Step 4 ：However, since the interval includes 0 but excludes 2π, the only solution in this interval is $\theta = 0$

Step 5 ：Final Answer: The solution to the equation $\sec \theta-1=0$ in the interval [0,2 \pi) is $\boxed{0}$