Simplify a rational trigonometric expression

The video tutorial explains how to simplify a trigonometric expression involving sine and cosine squared terms. It begins by introducing the problem and then applies trigonometric identities, specifically the Pythagorean identity, to convert sine squared into terms of cosine squared. The instructor demonstrates substitution and simplification techniques, leading to the final simplified expression, which equals one.

What is the initial trigonometric expression that needs to be simplified?

• sine squared of X plus cosine squared of X

• sine squared of X minus cosine squared of X

• cosine squared of X minus sine squared of X

• sine squared of X times cosine squared of X

Which trigonometric identity is used to convert sine squared into cosine squared terms?

• sine squared plus cosine squared equals 2

• sine squared minus cosine squared equals 1

• sine squared plus cosine squared equals 1

• sine squared times cosine squared equals 1

What is the expression for sine squared of X in terms of cosine squared of X?

• 1 plus cosine squared of X

• 1 minus cosine squared of X

• cosine squared of X minus 1

• 2 minus cosine squared of X

After substitution, what does the numerator of the expression become?

• 1 minus 2 cosine squared of X

• cosine squared of X minus 1

• 1 plus 2 cosine squared of X

• 2 minus cosine squared of X

What is the final simplified result of the trigonometric expression?

• Negative one

• Zero

• Two

• One