Factoring out a GCF in a trig identity

The video tutorial begins with a review of factoring in algebra, specifically focusing on the greatest common factor. The instructor then transitions to applying similar factoring techniques to trigonometric functions, demonstrating how to factor out terms like tangent squared. The lesson continues with the use of trigonometric identities to simplify expressions, highlighting the Pythagorean identities. The tutorial concludes with a simplification of expressions and a discussion on the beauty of mathematics.

What is the first step in factoring out the greatest common factor in algebra?

• Identify the terms that share a common factor

• Multiply all terms by the greatest common factor

• Add the terms together

• Divide each term by the smallest number

In trigonometry, what is the equivalent of factoring out a common factor?

• Factoring out tangent squared

• Subtracting sine from cosine

• Multiplying by the Pythagorean identity

• Adding sine and cosine

What is left over when you factor out tangent squared from itself?

• One minus sine squared

• Zero

• Cosine squared

• Sine squared

Which identity is used to simplify 1 - sine squared?

• Pythagorean identity

• Reciprocal identity

• Quotient identity

• Even-odd identity

Why is rewriting tangent as sine over cosine helpful?

• It changes the angle

• It makes the expression longer

• It allows for cancellation of terms

• It adds complexity to the problem