Find the Exact Value sec(pi/4)^2

Problem

sec(π/4)

Solution

1. Identify the trigonometric value for the base expression sec(π/4)

2. Recall the reciprocal identity sec(θ)=1/cos(θ)

3. Substitute the known value cos(π/4)=√(,2)/2

4. Calculate the secant value:

sec(π/4)=1/√(,2)/2

sec(π/4)=2/√(,2)

sec(π/4)=√(,2)

5. Square the resulting value to find the final answer:

(√(,2))2=2

Final Answer

sec(π/4)=2

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