Simplify sec(45)

Problem

sec(45)

Solution

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

sec(θ)=1/cos(θ)

2. Substitute the given angle of 45 into the identity.

sec(45)=1/cos(45)

3. Recall the exact value of cos(45) from the unit circle.

cos(45)=√(,2)/2

4. Substitute the value of the cosine into the expression and simplify the fraction.

sec(45)=1/√(,2)/2

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

sec(45)=2/√(,2)

sec(45)=(2√(,2))/2

sec(45)=√(,2)

Final Answer

sec(45)=√(,2)

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