Trigonometric Expression Simplification

The video tutorial explains how to simplify a given trigonometric expression to a single trigonometric function using two methods. The first method involves converting all trigonometric functions to sines and cosines and then simplifying the complex fraction by multiplying the numerator and denominator by the least common denominator. The second method involves finding a common denominator in the expression and simplifying by multiplying with the reciprocal. Both methods ultimately simplify the expression to the single trigonometric function cosine x.

What is the main goal when simplifying the given trigonometric expression?

• To eliminate all trigonometric functions

• To convert it into a polynomial

• To express it as a single trigonometric function

• To find the derivative of the expression

In the first method, what is tangent x converted into?

• Sine x times cosine x

• Cosine x divided by sine x

• Cosine x minus sine x

• Sine x divided by cosine x

What is the least common denominator used in the first method?

• Sine x plus cosine x

• Tangent x

• Cosine x

• Sine x

What common factor is factored out in the numerator during the first method?

• Sine x plus cosine x

• Tangent x

• Cosine x

• Sine x

What is the result of the first method of simplification?

• Cosine x

• Tangent x

• Secant x

• Sine x

In the second method, what is the first step after substituting tangent x?

• Multiply by cosine x

• Find a common denominator

• Factor out sine x

• Divide by sine x

How is the expression simplified in the second method?

• By adding fractions

• By dividing by sine x

• By multiplying by the reciprocal

• By subtracting fractions

What is the final result of the second method of simplification?

• Cosine x

• Sine x

• Cotangent x

• Tangent x

What does the fraction bar represent in the second method?

• Addition

• Subtraction

• Multiplication

• Division

What is the common factor that simplifies to one in both methods?

• Sine x minus cosine x

• Tangent x

• Cosine x minus sine x

• Sine x plus cosine x