Evaluate sec(-pi/4)^2

Problem

sec2(−π/4)

Solution

1. Apply the even-odd property of the secant function, which states sec(−θ)=sec(θ)

sec(−π/4)=sec(π/4)

2. Use the reciprocal identity for secant, where sec(θ)=1/cos(θ)

sec(π/4)=1/cos(π/4)

3. Substitute the known value for cos(π/4) which is √(,2)/2

sec(π/4)=1/√(,2)/2

4. Simplify the fraction to find the value of the secant term.

sec(π/4)=2/√(,2)

sec(π/4)=√(,2)

5. Square the result as required by the original expression.

(√(,2))2=2

Final Answer

sec2(−π/4)=2

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