How to simplify a trigonometric expression by squaring a binomial

The video tutorial explains how to expand and simplify the expression (sin X + cos X)^2 using the FOIL method. It demonstrates combining like terms and applying trigonometric identities to simplify the expression further. The tutorial concludes with the final simplified form of the expression, emphasizing the importance of understanding trigonometric identities in simplification.

What is the result of expanding (sin(x) + cos(x))^2 using the FOIL method?

• sin^2(x) + cos^2(x)

• sin^2(x) + 2sin(x)cos(x) + cos^2(x)

• 2sin(x)cos(x)

• sin(x) + cos(x)

Which trigonometric identity is used to simplify sin^2(x) + cos^2(x)?

• sin(x) + cos(x) = 1

• 1 + cot^2(x) = csc^2(x)

• sin^2(x) + cos^2(x) = 1

• tan^2(x) + 1 = sec^2(x)

What is the simplified form of sin^2(x) + 2sin(x)cos(x) + cos^2(x)?

• 2sin(x)cos(x)

• 1 + 2sin(x)cos(x)

• sin(x) + cos(x)

• 1

Why is it important to keep the squared terms in the expression (sin(x) + cos(x))^2?

• They simplify to zero.

• They are used to find the derivative.

• They can be ignored.

• They are necessary for the identity sin^2(x) + cos^2(x) = 1.

What does the expression sin^2(x) + cos^2(x) equal?

• 0

• 2

• 1

• sin(x)cos(x)