Trigonometric Expressions and Factorization

The video tutorial covers solving a trigonometry identity problem. It begins with an introduction to the problem and proceeds to expand sin 2x. The instructor then applies trigonometric identities, such as sin squared x plus cos squared x equals 1, to simplify the expression. Factorization techniques are used to further simplify the problem, followed by rearranging terms. The tutorial concludes with the final solution, verifying that the left-hand side equals the right-hand side.

What is the first step suggested in solving the trigonometry question?

• Guess the answer

• Use a calculator

• Start from the right-hand side

• Start from the left-hand side

What is the common mistake to avoid when dealing with trigonometric identities?

• Using the wrong identity

• Not using a calculator

• Ignoring the question

• Starting from the right-hand side

What should you do when you encounter sin 2x in a problem?

• Ignore it

• Use a calculator

• Expand it using a known identity

• Convert it to cos 2x

What is the expanded form of sin 2x?

• sin^2 x + cos^2 x

• 2 sin x cos x

• sin x + cos x

• 1 - 2 sin x cos x

What identity is recalled from grade 11 to help solve the problem?

• cos^2 x - sin^2 x = 1

• sin x = cos x

• tan^2 x + 1 = sec^2 x

• sin^2 x + cos^2 x = 1

Why was the identity sin^2 x + cos^2 x = 1 used in this problem?

• It was a random choice

• It simplifies the problem

• It was required by the question

• It was the only option left

What is the significance of the expression sin^2 x + cos^2 x in trigonometry?

• It is always equal to 0

• It is always equal to 1

• It is always equal to -1

• It is always equal to 2

What should you do if you get stuck while solving a trigonometric problem?

• Ask for help

• Give up

• Try a different approach

• Use a calculator

What is the rearranged form of the expression before factorization?

• sin^2 x + cos^2 x

• sin x + cos x

• sin^2 x - 2 sin x cos x + cos^2 x

• 2 sin x cos x

What is the factorized form of x^2 - 2xy + y^2?

• (x - y)(x + y)

• (x + y)(x - y)

• (x - y)(x - y)

• (x + y)(x + y)