Algebra and Trigonometry: Double Angle, Half Angle, and Reduction Formulas

The video tutorial covers trigonometric identities, focusing on double angle, half angle, and reduction formulas. It explains how to derive these identities using Pythagorean identities and provides example problems to illustrate their application. The tutorial also includes advanced simplifications and verifications of trigonometric identities, offering a comprehensive understanding of these mathematical concepts.

Which identity is used to derive the reduction identities from the double angle identity for cosine?

• Pythagorean identity

• Quotient identities

• Sum and difference identities

• Product-to-sum identities

What is the result of simplifying the expression 2 sine(pi/4) cosine(pi/4) using double angle identities?

• cosine(pi/2)

• sine(pi/4)

• sine(pi/2)

• tangent(pi/2)

In the context of double angle identities, what is the value of cosine(2x) if sine(x) = 1/8?

• 1/4

• 3/4

• 1/2

• 31/32

How do you determine the sign of a trigonometric function when using half angle identities?

• By using the sum and difference identities

• By checking the quadrant of the half angle

• By using the Pythagorean identity

• By checking the quadrant of the original angle

What is the simplified form of the expression using the half angle identity for sine(11pi/12)?

• sqrt(2 - sqrt(3))/2

• sqrt(3 + sqrt(2))/2

• sqrt(3 - sqrt(2))/2

• sqrt(2 + sqrt(3))/2

What is the result of simplifying the expression 2cos²(37°) - 1 using trigonometric identities?

• cos(37°)

• cos(74°)

• sin(37°)

• tan(37°)

Which identity is used to verify that 2sin(x)cos(x) is equivalent to sin(2x)?

• Half Angle Identity

• Double Angle Identity

• Pythagorean Identity

• Sum of Angles Identity

How can the expression cos²(x) - sin²(x) be simplified using trigonometric identities?

• cos(2x)

• sin(2x)

• tan(2x)

• 1 - 2sin²(x)

What is the simplified form of the expression (1 - cos(2x))(1 + cos(2x))?

• 1 - sin²(2x)

• cos²(2x)

• 1 - cos²(2x)

• sin²(2x)

Which identity is used to simplify the expression 1 - 2cos²(x) + cos(4x)?

• Half Angle Identity

• Sum of Angles Identity

• Pythagorean Identity

• Double Angle Identity