Understanding Sum and Difference Identities

The video tutorial explains how to find the function F(x) by applying the sum and difference identity for sine to a given equation. The process involves simplifying the expression by combining like terms and matching it to the original equation. The solution reveals that F(x) equals cosine X, emphasizing the importance of understanding and applying trigonometric identities.

What is the main goal of the problem discussed in the video?

• To calculate the value of FX

• To solve for sin y

• To determine the function F(x)

• To find the value of Y

Which identity is applied to the left side of the equation first?

• Product identity

• Difference identity for sine

• Quotient identity

• Sum identity for sine

What is the first step in applying the sum identity for sine?

• Adding the angles

• Multiplying the angles

• Dividing the angles

• Subtracting the angles

What is the result of applying the difference identity for sine?

• cosine x * sin y - sin x * cosine y

• sin x * sin y

• cosine x * cosine y

• sin x * cosine y - cosine x * sin y

What happens when you combine like terms in the expression?

• The terms are halved

• The terms double

• The terms remain unchanged

• The terms cancel out

What is the final expression obtained after simplification?

• sin x * cosine y

• cosine x * sin y

• 2 * cosine x * sin y

• 2 * sin x * sin y

What does F(x) equal in the final result?

• tan x

• cosine x

• cot x

• sin x

Why is it important to apply the sum and difference identities correctly?

• To simplify the equation to match the right side

• To determine the value of FX

• To find the value of y

• To ensure the equation is balanced

What is the significance of the term 2 * cosine x * sin y in the context of the problem?

• It is the value of Y

• It is the value of F(x)

• It is the simplified form of the left side

• It represents the original problem

What is the key takeaway from the video?

• Understanding the product identity

• Mastering the sum and difference identities for sine

• Learning to solve for Y

• Finding the value of FX