Evaluate tangent for the difference of two angles and simplify, tan

The video tutorial explains how to use the tangent difference formula to evaluate the tangent of 225 degrees minus the tangent of 30 degrees. It begins by identifying the angles on the unit circle and calculating their tangent values. The tutorial then demonstrates how to substitute these values into the tangent difference formula and simplify the resulting expression using algebraic techniques, including rationalizing the denominator.

What is the first step in using the tangent difference formula?

• Identify the angles U and V

• Calculate the sine of the angles

• Find the cosine of the angles

• Directly substitute into the formula

What is the tangent of 225 degrees?

• -1

• sqrt(3)/3

• 0

• 1

How do you rationalize the denominator for the tangent of 30 degrees?

• Multiply by 3/sqrt(3)

• Multiply by 2

• Multiply by 1/2

• Multiply by sqrt(3)/3

What is the formula for the tangent of (U - V)?

• (tan U - tan V) / (1 - tan U * tan V)

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

• (tan U + tan V) / (1 + tan U * tan V)

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

What is the result of multiplying the top and bottom of a fraction by the same number?

• The fraction becomes zero

• The fraction halves

• The fraction remains unchanged

• The fraction doubles

What is the final simplified form of the expression for the tangent difference?

• 2 - sqrt(3)

• 3 + sqrt(3)

• 1 + sqrt(3)

• 2 + sqrt(3)

What algebraic technique is used to simplify the expression in the final step?

• Completing the square

• Rationalizing the denominator

• Factoring

• Expanding