Solve for x sec(x)=-1

Problem

sec(x)=−1

Solution

1. Rewrite the equation using the reciprocal identity for the secant function, which is sec(x)=1/cos(x)

1/cos(x)=−1

2. Solve for cos(x) by taking the reciprocal of both sides of the equation.

cos(x)=−1

3. Identify the values of x on the unit circle where the x-coordinate is −1

x=π

4. Generalize the solution to include all possible angles by adding integer multiples of the period 2*π where n is any integer.

x=π+2*n*π

Final Answer

sec(x)=−1⇒x=π+2*n*π

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