Trigonometric Identities and Simplifications

The video tutorial explains how to simplify a trigonometric expression involving secant and cosine. It begins by converting secant to cosine, then simplifies the expression using reciprocal identities. The tutorial further simplifies the expression using trigonometric identities, specifically the relationship between tangent and secant. Finally, it provides a caution about correctly inputting the simplified result into a homework system.

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

• Cosecant x divided by sine x minus one

• Tangent x divided by sine x minus one

• Cosine x divided by sine x minus one

• Secant x divided by sine x minus one

What is the equivalent expression for secant x in terms of cosine?

• Sine x

• Cosine x

• 1 / cosine x

• 1 / sine x

How do you rewrite the expression when dividing by cosine x?

• Subtract cosine x

• Multiply by cosine x

• Multiply by the reciprocal of cosine x

• Add cosine x

What is the result of multiplying 1 over cosine x by cosine x?

• Cosine x

• Secant x

• Cosine 2x

• Sine x

Which identity is used to further simplify secant 2x - 1?

• Sine identity

• Cosine identity

• Tangent identity

• Cosecant identity

What does secant 2x - 1 simplify to using the tangent identity?

• Sine x

• Cosine x

• Tangent x

• Cosecant x

What should you be cautious about when entering the simplified expression into a homework system?

• Entering the expression as secant x

• Entering the expression as cosine x

• Entering the expression as sine x

• Entering the expression as tangent 2x

What is the correct way to enter tangent 2x in the homework system?

• Cosine x

• Sine x

• Tangent x

• Tangent x squared

What is the final simplified form of the expression?

• Tangent x

• Cosine x

• Sine x

• Secant x