Trigonometric Identities and Simplifications

The video tutorial explains how to simplify a trigonometric expression to a single trig function using two methods. The first method involves simplifying the fraction and using trigonometric identities, while the second method uses a common denominator approach. Both methods ultimately simplify the expression to secant squared x. The tutorial emphasizes understanding and applying trigonometric identities effectively.

What is the main goal of the video tutorial?

• To simplify a trigonometric expression to a single function

• To calculate the area of a triangle

• To learn how to solve quadratic equations

• To understand the Pythagorean theorem

In the first method, what is the first step to simplify the fraction?

• Subtract the denominator from the numerator

• Add the numerator and the denominator

• Multiply the numerator by the denominator

• Divide each term in the numerator by the denominator

Which trigonometric identity is used to simplify two over cosine squared x?

• Sine squared theta plus cosine squared theta equals one

• One over cosine theta equals secant theta

• Sine theta divided by cosine theta equals tangent theta

• Tangent squared theta plus one equals secant squared theta

What is the result of simplifying two secant squared x minus one secant squared x?

• Sine squared x

• Cosine squared x

• Secant squared x

• Tangent squared x

In the second method, how is one rewritten to obtain a common denominator?

• As sine squared x over sine squared x

• As cosine squared x over cosine squared x

• As tangent squared x over tangent squared x

• As secant squared x over secant squared x

What is the common denominator used in the second method?

• Secant squared x

• Cosine squared x

• Tangent squared x

• Sine squared x

Which identity is used to simplify the numerator in the second method?

• One over sine theta equals cosecant theta

• Tangent squared theta plus one equals secant squared theta

• Sine squared theta plus cosine squared theta equals one

• Cosine theta divided by sine theta equals cotangent theta

What is the final simplified form of the expression using the second method?

• Sine squared x

• Cosine squared x

• Secant squared x

• Tangent squared x

What is the equivalent expression for one over cosine squared x?

• Cotangent squared x

• Secant squared x

• Tangent squared x

• Sine squared x

What is the purpose of factoring out negative one in the second method?

• To eliminate the denominator

• To convert the expression to sine and cosine

• To simplify the expression using identities

• To change the sign of the entire expression