Evaluate sec(45 degrees )

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 or a special right triangle.

cos(45^∘)=√(,2)/2

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

sec(45^∘)=1/√(,2)/2

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

sec(45^∘)=2/√(,2)

sec(45^∘)=√(,2)

Final Answer

sec(45^∘)=√(,2)

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