Don't get rid of your denominators, combine them

This video tutorial explains how to combine denominators in trigonometric fractions without rationalizing them. It covers finding common denominators by multiplying existing ones, using trigonometric identities like the Pythagorean identities, and simplifying expressions by rewriting them in terms of sines and cosines. The tutorial emphasizes the importance of understanding trigonometric identities to simplify complex expressions effectively.

What is the main goal when dealing with fractions that have trigonometric denominators?

• To rationalize the denominator

• To convert them to decimals

• To combine the fractions

• To eliminate the numerators

What is the quickest way to find a common denominator for fractions with different denominators?

• Subtract the denominators

• Multiply the denominators

• Add the denominators

• Divide the denominators

Which trigonometric identity is used to simplify secant squared minus one?

• Sine squared

• Tangent squared

• Cosine squared

• Cotangent squared

How can you express secant in terms of sine and cosine?

• cosine/sine

• sine/cosine

• 1/cosine

• 1/sine

What is the reciprocal of sine squared divided by cosine squared?

• Cosine squared divided by sine squared

• Sine squared divided by cosine squared

• Tangent squared

• Cotangent squared

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

• 2 sine and cosine

• 2 cotangent and cosecant

• 2 cosine and sine

• 2 tangent and secant

Why is it important to know trigonometric identities when simplifying expressions?

• They are not necessary

• They make calculations longer

• They complicate the process

• They simplify the process