Solve for x sec(x)- square root of 2=0

Problem

sec(x)−√(,2)=0

Solution

1. Isolate the trigonometric function by adding √(,2) to both sides of the equation.

sec(x)=√(,2)

2. Rewrite the equation in terms of the cosine function using the reciprocal identity sec(x)=1/cos(x)

1/cos(x)=√(,2)

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

cos(x)=1/√(,2)

4. Rationalize the denominator to identify the standard value on the unit circle.

cos(x)=√(,2)/2

5. Determine the general solutions for x where the cosine is positive √(,2)/2 which occurs in Quadrants I and IV.

x=π/4+2*n*π

x=(7*π)/4+2*n*π

Final Answer

sec(x)−√(,2)=0⇒x=π/4+2*n*π,(7*π)/4+2*n*π

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