Learn how to find the exact value of an angle using sum formula for tangent

The video tutorial explains how to use the tangent formula for the sum of two angles, specifically π/6 and π/4, to find the tangent of 5π/12. The instructor guides through identifying and replacing angles, evaluating tangent values, and simplifying the expression using algebraic techniques. The tutorial concludes with a final simplified expression and checks for accuracy.

What is the formula for the tangent of the sum of two angles U and V?

• tan(U + V) = (tan(U) + tan(V)) / (1 - tan(U)tan(V))

• tan(U + V) = tan(U) + tan(V)

• tan(U + V) = tan(U) - tan(V)

• tan(U + V) = (tan(U) - tan(V)) / (1 + tan(U)tan(V))

What is the tangent of π/6?

• sqrt(3)/3

• 1/2

• sqrt(3)

• 1

What is the tangent of π/4?

• 1

• sqrt(2)/2

• sqrt(2)

• 0

What is the purpose of multiplying by 3/3 in the simplification process?

• To convert to degrees

• To find a common denominator

• To change the angle

• To eliminate the fraction in the numerator

What is the next step after multiplying by 3/3 in the simplification process?

• Add the angles

• Multiply by the conjugate

• Divide by 2

• Subtract the angles

What is the final simplified form of the expression?

• 2 + sqrt(3)/3

• 3 + sqrt(3)/3

• 2 + sqrt(3)/6

• 3 + sqrt(3)/2

Why is it important to use the conjugate in the simplification process?

• To convert to radians

• To find the tangent

• To eliminate the denominator

• To add the angles