Factor and use fundamental identities to simplify

The video tutorial explains how to simplify a trigonometric expression involving tangent and sine functions. It begins by introducing the problem and suggests using trigonometric identities for simplification. The instructor demonstrates factoring as a method to simplify expressions and applies Pythagorean identities to further reduce the expression. The tutorial concludes with a step-by-step simplification, resulting in a simplified trigonometric expression.

What is the initial expression that needs to be simplified in the video?

• Cosine squared of x minus sine squared of x

• Tangent squared of x plus sine squared of x

• Sine squared of x plus cosine squared of x

• Tangent squared of x minus tangent squared of x times sine squared of x

What is the purpose of factoring out common terms in an expression?

• To eliminate all trigonometric functions

• To simplify the expression by reducing repetition

• To make the expression more complex

• To increase the number of terms

Which identity is used to rewrite 1 minus sine squared of x?

• Sine squared of x plus cosine squared of x equals 1

• Sine squared of x equals 1 minus cosine squared of x

• Tangent squared of x equals sine squared of x over cosine squared of x

• Cosine squared of x equals 1 minus sine squared of x

How is tangent squared of x rewritten using the quotient identity?

• As sine squared of x divided by cosine squared of x

• As cosine squared of x divided by sine squared of x

• As sine squared of x plus cosine squared of x

• As sine squared of x times cosine squared of x

What is the final simplified form of the expression?

• Sine squared of x

• Cosine squared of x

• 1 minus sine squared of x

• Tangent squared of x