Math tutorial for using the sum of two angles formula for the tangent of 105 degrees

The video tutorial explains the tangent addition formula, demonstrating how to apply it by plugging in specific angle values. It covers the simplification of tangent values using known trigonometric identities and emphasizes the importance of understanding the unit circle. The tutorial concludes with a final simplification of the expression and a brief discussion on eliminating radicals from the denominator.

What is the formula for the tangent of the sum of two angles?

• tangent(U + V) = (tangent U + tangent V) / (1 - tangent U * tangent V)

• tangent(U + V) = (tangent U + tangent V) / (1 + tangent U * tangent V)

• tangent(U + V) = (tangent U - tangent V) / (1 + tangent U * tangent V)

• tangent(U + V) = (tangent U * tangent V) / (1 + tangent U + tangent V)

When substituting angles into the tangent addition formula, what are the angles used in the example?

• 30 and 45 degrees

• 60 and 30 degrees

• 60 and 45 degrees

• 45 and 30 degrees

What is the simplified value of tangent 60 degrees?

• 2

• 1

• sqrt 3

• sqrt 3 / 3

What is the simplified value of tangent 45 degrees?

• 0

• sqrt 2

• 1

• sqrt 3

Why is it important to recognize tangent values quickly during simplification?

• To avoid drawing the unit circle

• To save time during exams

• To ensure accuracy in calculations

• All of the above

What technique is used to remove radicals from the denominator?

• Dividing by a factor

• Adding a constant

• Multiplying by the conjugate

• Using the unit circle

What is the final simplified expression after removing radicals from the denominator?

• 1 + sqrt 3

• -2 - sqrt 3

• -1 - sqrt 3

• 2 + sqrt 3