Trigonometric Identities and Functions

The video tutorial explains how to simplify a given trigonometric expression to a single expression without fractions. It begins by applying negative angle identities for cotangent, cosine, and sine. The tutorial then rewrites cotangent in terms of sines and cosines, finds a common denominator for subtraction, and simplifies the expression to -cosecant X.

What is the negative angle identity for cotangent?

• cot(-x) = -1/cot(x)

• cot(-x) = -cot(x)

• cot(-x) = cot(x)

• cot(-x) = 1/cot(x)

How can cotangent be expressed in terms of sine and cosine?

• cot(x) = cos(x)/sin(x)

• cot(x) = sin(x)/cos(x)

• cot(x) = 1/sin(x)

• cot(x) = 1/cos(x)

What is the common denominator used for the subtraction in the expression?

• sec(x)

• sin(x)

• tan(x)

• cos(x)

What is the result of subtracting -cos^2(x)/sin(x) and -sin^2(x)/sin(x)?

• (cos^2(x) + sin^2(x))/sin(x)

• -(cos^2(x) - sin^2(x))/sin(x)

• (cos^2(x) - sin^2(x))/sin(x)

• -(cos^2(x) + sin^2(x))/sin(x)

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

• cos^2(x) + sin^2(x) = 0

• cos^2(x) + sin^2(x) = 2

• cos^2(x) + sin^2(x) = 1

• cos^2(x) + sin^2(x) = -1

What is the simplified form of -1/sin(x)?

• -sec(x)

• -tan(x)

• -cot(x)

• -cosec(x)

Which trigonometric function is equivalent to 1/sin(x)?

• sec(x)

• cot(x)

• tan(x)

• cosec(x)

What is the final simplified expression of the given trigonometric problem?

• -sec(x)

• -cot(x)

• -cosec(x)

• -tan(x)