Simplifying Complex Fractions and Trigonometric Functions

The video tutorial explains how to simplify a trigonometric expression into a product of trig functions. It begins with an introduction to the problem and explores substitution and conversion to sine and cosine. The tutorial then addresses simplifying complex fractions by using the least common denominator. Further simplification is achieved through factoring, leading to the final expression in product form. The tutorial concludes by ensuring the expression is in alphabetical order with a multiplication sign.

What is the initial substitution attempted for tangent in the expression?

• Tangent is replaced with cotangent.

• Tangent is replaced with cosine.

• Tangent is replaced with secant minus one.

• Tangent is replaced with sine.

What is the purpose of converting trigonometric functions to sine and cosine?

• To make the expression more complex.

• To change the expression to a different function.

• To simplify the expression.

• To eliminate all trigonometric functions.

What is a complex fraction?

• A fraction that cannot be simplified.

• A fraction that contains fractions in the numerator or denominator.

• A fraction with a large denominator.

• A fraction with a large numerator.

How do you simplify a complex fraction?

• By dividing the numerator by the denominator.

• By converting to decimals.

• By adding fractions.

• By multiplying the top and bottom by the least common denominator.

What is the least common denominator used in the simplification?

• Sine x

• Tangent x

• Cosine 2x

• Cosine x

What common factor is found in the numerator and denominator during simplification?

• Cosine x + Sine x

• Sine x - Cosine x

• Cosine x

• Sine x

What is the result after canceling the common factor in the expression?

• Secant x

• Sine x / Cosine 2x

• Cosine 2x / Sine x

• Tangent x

How is the expression finally written as a product of trigonometric functions?

• Cosine x times Tangent x

• Sine x times Tangent x

• Cosine x times Sine x

• Sine x times Cosine x

Why is it important to write the functions in alphabetical order?

• To ensure consistency.

• To follow the instructions given.

• To match the original expression.

• To make it easier to read.

What is the final simplified expression?

• Cosine x times Sine x

• Sine x times Tangent x

• Cosine x times Tangent x

• Sine x times Cosine x