Trigonometric Expressions and Identities

The video tutorial explains how to simplify a trigonometric expression by finding a common denominator for two fractions. It involves multiplying the numerators and denominators by specific trigonometric expressions to achieve a common denominator. The tutorial then demonstrates distributing and simplifying both the numerator and the denominator. It uses trigonometric identities to substitute and simplify the expression further, resulting in a final simplified form of the expression. The video concludes with a brief summary of the steps taken.

What is the first step in simplifying the given trigonometric expression?

• Find a common denominator

• Use trigonometric identities

• Add the fractions

• Multiply by conjugates

What do we multiply the numerator and denominator of the first fraction by?

• One minus sine x

• One plus sine x

• Cosine x

• Tangent x

What is the common denominator achieved in the process?

• Product of one plus sine x and one minus sine x

• One minus sine x

• One plus sine x

• Cosine squared x

After setting up the common denominator, what is the next step?

• Add the numerators

• Use the Pythagorean identity

• Distribute and combine like terms

• Multiply by cosine

What is the result of distributing two in the numerator?

• Two plus two sine x

• Two minus two sine x

• Zero

• Four sine x

What happens to the terms two minus two in the numerator?

• They cancel each other out

• They add up to four

• They multiply to zero

• They remain unchanged

What identity is used to replace one minus sine squared x?

• Tangent squared theta

• Secant squared theta

• Cosine squared theta

• Sine squared theta

What is the result of sine x minus sine x in the denominator?

• Cosine squared x

• One

• Zero

• Sine squared x

What is the simplified form of four sine x divided by cosine squared x?

• Four secant x times tangent x

• Four cosine x times sine x

• Four sine x times cosine x

• Four tangent x times secant x

What trigonometric function is equivalent to sine x divided by cosine x?

• Cotangent x

• Secant x

• Tangent x

• Cosecant x