Trigonometric Simplification Techniques

The video tutorial guides viewers through simplifying a trigonometric expression. It begins with selecting an identity for the expression (1 - cos(2x))/sin(x). The tutorial uses substitution to express cos(2x) in terms of sine, simplifies the expression by distributing a negative, and reduces it to 2sin(x). The final step is to match this simplified expression with the given options, selecting 2sin(x) as the correct identity.

What is the initial expression given in the problem?

• 1 - cos(2x) / sin(x)

• cos(2x) - 1 / sin(x)

• sin(x) / (1 - cos(2x))

• 1 + cos(2x) / sin(x)

Which identity is used to substitute for cos(2x)?

• cos(2x) = cos^2(x) - sin^2(x)

• cos(2x) = 2cos^2(x) - 1

• cos(2x) = 2sin^2(x) - 1

• cos(2x) = 1 - 2sin^2(x)

What is the expression after substituting for cos(2x)?

• 1 + 2sin^2(x) / sin(x)

• 1 - (1 - 2sin^2(x)) / sin(x)

• 1 + (1 - 2sin^2(x)) / sin(x)

• 1 - 2sin^2(x) / sin(x)

What is the result of distributing the negative sign in the expression?

• 1 - 1 + 2sin^2(x)

• 1 + 1 - 2sin^2(x)

• 1 - 1 - 2sin^2(x)

• 1 + 1 + 2sin^2(x)

What is the expression after simplifying 1 - 1?

• 2sin^2(x) / sin(x)

• sin^2(x) / sin(x)

• 2sin(x) / sin(x)

• sin(x) / sin(x)

What common factor is canceled in the expression?

• cos(x)

• sin(x)

• cot(x)

• tan(x)

What is the expression after canceling the common factor?

• cos(x)

• 2cos(x)

• sin(x)

• 2sin(x)

What is the final simplified expression?

• cos(x)

• 2sin(x)

• 2cos(x)

• sin(x)

Which option matches the final simplified expression?

• 2sin(x)

• 2cos(x)

• sin(x)

• cos(x)

What is the purpose of the simplification process in this problem?

• To prove a mathematical theorem

• To solve for x

• To derive a new trigonometric identity

• To find a matching identity from the list