What is the value of sec(tan^(-1)(1/√3))?

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Q: What is the value of sec(tan^(-1)(1/√3))?

Solution: Using the triangle with opposite = 1 and adjacent = √3, hypotenuse = 2. Thus, sec(tan^(-1)(1/√3)) = 2.

Steps: 7

Step 1: Understand that tan^(-1)(1/√3) means we are looking for an angle whose tangent is 1/√3.
Step 2: Recall that tangent is defined as opposite side over adjacent side in a right triangle.
Step 3: Set up a right triangle where the opposite side is 1 and the adjacent side is √3.
Step 4: Use the Pythagorean theorem to find the hypotenuse. The hypotenuse = √(1^2 + (√3)^2) = √(1 + 3) = √4 = 2.
Step 5: The secant function (sec) is defined as the hypotenuse over the adjacent side. So, sec(angle) = hypotenuse / adjacent.
Step 6: Substitute the values: sec(tan^(-1)(1/√3)) = 2 / √3.
Step 7: Since we are looking for sec(tan^(-1)(1/√3)), we find that sec(tan^(-1)(1/√3)) = 2.