Trigonometric Identities and Formulas

The video tutorial covers the sum and difference formulas for trigonometric functions: cosine, sine, and tangent. It explains how to apply these formulas to solve problems involving specific angles, such as 15 degrees, 105 degrees, and others. The tutorial provides step-by-step examples to demonstrate the application of these formulas in evaluating trigonometric expressions.

What is the correct formula for cosine of alpha plus beta?

• tan(alpha) + tan(beta)

• cos(alpha)cos(beta) - sin(alpha)sin(beta)

• cos(alpha)cos(beta) + sin(alpha)sin(beta)

• sin(alpha)cos(beta) + cos(alpha)sin(beta)

Which angles can be used to evaluate sine of 15 degrees using the sum and difference formulas?

• 45 and 60

• 30 and 45

• 45 and 30

• 60 and 90

How do you evaluate sine of 105 degrees using the sum and difference formulas?

• Using angles 45 and 60

• Using angles 90 and 15

• Using angles 30 and 75

• Using angles 60 and 45

What is the result of cosine of 2π/3 minus π/6?

• 1/2

• √3/2

• 0

• 1

Which formula is used to evaluate cosine of 5π/12?

• tan(alpha) - tan(beta)

• sin(alpha)cos(beta) - cos(alpha)sin(beta)

• cos(alpha)cos(beta) + sin(alpha)sin(beta)

• cos(alpha)cos(beta) - sin(alpha)sin(beta)

What is the value of cosine 70 degrees times cosine 40 degrees plus sine 70 degrees times sine 40 degrees?

• sine of 110 degrees

• cosine of 30 degrees

• sine of 30 degrees

• cosine of 110 degrees

How do you simplify cosine 20 times cosine 40 minus sine 20 times sine 40?

• cosine of 20 degrees

• sine of 60 degrees

• cosine of 60 degrees

• sine of 20 degrees

What is the value of sine 5π/12 times cosine π/12 minus cosine 5π/12 times sine π/12?

• cosine of π/6

• cosine of π/3

• sine of π/3

• sine of π/6

Which formula is used to evaluate tangent of 15 degrees?

• tan(alpha) + tan(beta) / 1 - tan(alpha)tan(beta)

• tan(alpha) - tan(beta) / 1 + tan(alpha)tan(beta)

• tan(alpha)tan(beta) / 1 + tan(alpha) + tan(beta)

• tan(alpha) + tan(beta) / 1 + tan(alpha)tan(beta)

What is the simplified form of the expression for tangent 15 degrees?

• 2 + √3

• 2 - √3

• √3 + 2

• √3 - 2