Simplify sec(pi/4)

Problem

sec(π/4)

Solution

1. Identify the definition of the secant function in terms of the cosine function.

sec(x)=1/cos(x)

2. Substitute the given angle into the identity.

sec(π/4)=1/cos(π/4)

3. Recall the exact value of the cosine of π/4 from the unit circle.

cos(π/4)=√(,2)/2

4. Simplify the fraction by taking the reciprocal of the cosine value.

sec(π/4)=2/√(,2)

5. Rationalize the denominator by multiplying the numerator and denominator by √(,2)

sec(π/4)=(2√(,2))/2

6. Cancel the common factor of 2.

sec(π/4)=√(,2)

Final Answer

sec(π/4)=√(,2)

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