Trigonometric Identities and Simplifications

The video tutorial explains how to simplify a trigonometric expression by adding fractions with a common denominator. It begins with an expression in terms of sine and cosine, and guides through finding a common denominator, combining fractions, and simplifying using trigonometric identities. The process concludes with the expression simplified to 2 cosecant theta, emphasizing the importance of careful manipulation and understanding of trigonometric identities.

What is the first step in simplifying a trigonometric expression when no functions are squared?

• Convert all functions to tangent and cotangent

• Find a common denominator for fractions

• Use the Pythagorean identity

• Multiply all terms by cosine

When adding fractions, what must be true about their denominators?

• They must be equal

• They must be different

• They must be multiplied by sine

• They must be squared

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

• To eliminate the fractions

• To create a common denominator

• To simplify the expression

• To convert to tangent

What is the common denominator used in the example?

• 1 + cosine theta

• 1 + sine theta

• cosine theta

• sine theta x (1 + cosine theta)

What operation is performed after finding a common denominator?

• Subtract the numerators

• Divide the numerators

• Multiply the numerators

• Add the numerators

What identity is used to simplify sine squared theta + cosine squared theta?

• sine squared theta = 1

• cosine squared theta = 1

• sine squared theta + cosine squared theta = 1

• sine theta = cosine theta

What is the result of factoring out a common factor from the numerator?

• 1 + sine theta

• 1 + cosine theta

• 2

• cosine theta

What is the final simplified form of the expression in terms of trigonometric functions?

• 2 tangent theta

• 2 cosecant theta

• 2 cosine theta

• 2 sine theta

What is the result of 1 + cosine theta divided by 1 + cosine theta?

• 1

• sine theta

• cosine theta

• 0

What trigonometric function is equivalent to 1/sine theta?

• Cosecant theta

• Secant theta

• Cotangent theta

• Tangent theta