Simplifying Trigonometric Expressions

The video tutorial explains how to simplify a trigonometric expression by rewriting it in terms of sine and cosine. It discusses the use of substitution and finding a common denominator to simplify the expression. The tutorial demonstrates converting a division problem into a multiplication problem by using the reciprocal, ultimately simplifying the expression to a single trigonometric function, sine theta.

What is the primary goal when simplifying a trigonometric expression?

• To express it in terms of multiple trigonometric functions

• To convert it into a polynomial

• To express it in terms of a single trigonometric function

• To eliminate all trigonometric functions

Why is there no obvious substitution using Pythagorean identities in this expression?

• Because the expression contains only sine and cosine

• Because the expression is a polynomial

• Because the trigonometric functions are not squared

• Because the expression is already simplified

What is the benefit of expressing trigonometric expressions in terms of sine and cosine?

• It makes the expression more complex

• It converts the expression into a polynomial

• It simplifies the expression

• It eliminates trigonometric functions

What substitution is made for cosecant theta in the expression?

• One divided by tangent theta

• One divided by cotangent theta

• One divided by sine theta

• One divided by cosine theta

What is the common denominator used to add the fractions in the expression?

• Cosecant theta

• Sine theta

• Tangent theta

• Cosine theta

Why can't the sine theta terms be simplified across addition?

• Because they are not like terms

• Because they are already simplified

• Because addition prevents simplification

• Because they are in different fractions

How is the division problem converted into a multiplication problem?

• By multiplying by the original fraction

• By using the reciprocal of the fraction

• By adding the fractions

• By subtracting the fractions

What is the significance of using the reciprocal in simplifying the expression?

• It complicates the expression

• It helps in converting division to multiplication

• It eliminates the need for a common denominator

• It changes the trigonometric function

What happens to the expression when the numerator and denominator are the same?

• It simplifies to zero

• It remains unchanged

• It becomes undefined

• It simplifies to one

What is the final simplified form of the expression?

• Cosecant theta

• Sine theta

• Tangent theta

• Cosine theta