Simplifying Trigonometric Expressions

The video tutorial explains how to simplify a trigonometric expression by adding two fractions. It involves finding a common denominator, multiplying numerators and denominators, and simplifying the expression by clearing parentheses and combining like terms. The final step includes using a trigonometric identity to substitute and simplify the expression to its simplest form, resulting in four secant x.

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

• Substitute trigonometric identities

• Add the two fractions

• Multiply the fractions

• Divide the fractions

How do you obtain a common denominator for the given fractions?

• Multiply both fractions by the same binomial

• Add a constant to both fractions

• Divide the fractions by a common factor

• Multiply the numerator and denominator of each fraction by different binomials

Which binomial is used to multiply the numerator and denominator of the first fraction?

• Tangent x minus secant x

• Tangent x plus secant x

• Secant x minus tangent x

• Secant x plus tangent x

What is the purpose of multiplying the numerator and denominator by specific binomials?

• To change the expression completely

• To obtain a common denominator

• To simplify the expression directly

• To eliminate the fractions

What is the result of distributing the number 2 in the numerator?

• Four secant x minus four tangent x

• Two secant x plus two tangent x

• Four secant x plus four tangent x

• Two secant x minus two tangent x plus two secant x plus two tangent x

What happens to the terms negative secant x tangent x and secant x tangent x in the denominator?

• They add up to a positive value

• They cancel each other out

• They remain unchanged

• They multiply to give a new term

What is the simplified form of the numerator after combining like terms?

• Two secant x

• Zero

• Four secant x

• Two tangent x

Which trigonometric identity is used to simplify the denominator?

• Sine squared theta plus cosine squared theta equals one

• Tangent squared theta plus one equals secant squared theta

• Cosine squared theta minus sine squared theta equals one

• Secant squared theta minus tangent squared theta equals one

What is the final simplified form of the given expression?

• Two secant x

• Four tangent x

• Four secant x

• Zero

What is the significance of the identity secant squared theta minus tangent squared theta equals one?

• It is used to find a common denominator

• It is used to simplify the denominator

• It is irrelevant to the problem

• It helps in simplifying the numerator