Add and subtract fractions with unlike denominators for trigonometric expressions

The video tutorial explains how to add rational functions with unlike denominators by finding the least common denominator (LCD). It starts with a numerical example of adding 3/4 and 2/5, demonstrating the process of finding the LCD and converting fractions. The tutorial then extends this concept to trigonometric functions, showing how to combine fractions like 1/sin(Theta) and 1/cos(Theta) using the product of the terms as the LCD. Another example involves combining fractions with trigonometric expressions, emphasizing the importance of finding the LCD and multiplying appropriately to combine the fractions.

What is the least common denominator (LCD) when adding the fractions 3/4 and 2/5?

• 25

• 10

• 15

• 20

When combining 1/sin(Theta) and 1/cos(Theta), what is the least common denominator?

• sin^2(Theta) + cos^2(Theta)

• sin(Theta) + cos(Theta)

• sin(Theta) * cos(Theta)

• 1

In the example of combining cosine(Theta)/(1-sin(Theta)) and 2/cos(Theta), what is the least common denominator?

• cos(Theta) * (1 - sin(Theta))

• cos(Theta) * (1 + sin(Theta))

• cos^2(Theta)

• 1 - sin(Theta)

What is the result of multiplying the numerator by the LCD in the example of combining cosine(Theta)/(1-sin(Theta)) and 2/cos(Theta)?

• cos^2(Theta) + sin(Theta)

• cos^2(Theta) - 2 + sin(Theta)

• cos^2(Theta) + 2 - sin(Theta)

• 2cos(Theta) - sin(Theta)

What is the next step after finding the LCD and combining the expressions in trigonometric functions?

• Divide by the numerator

• Simplify the expression

• Multiply by another fraction

• Add a constant