Trigonometric Expression Simplification

The video tutorial explains how to simplify a trigonometric expression by converting all terms to sines and cosines. It demonstrates finding a common denominator, factoring, and simplifying the expression step-by-step. The process involves converting tangent to sine over cosine, finding a common denominator, factoring out common terms, and simplifying the expression to its simplest form, which is cosine x.

What is the first step in simplifying the given trigonometric expression?

• Convert everything to sines and cosines

• Multiply by the reciprocal

• Add a constant

• Divide by a constant

How is tangent x expressed in terms of sine and cosine?

• sine x times cosine x

• sine x divided by cosine x

• cosine x times sine x

• cosine x divided by sine x

What is the common denominator used in the expression?

• tangent x

• cosine x

• sine x

• secant x

What common factor is factored out from the numerator?

• tangent x

• sine x

• secant x

• cosine x

What operation is performed to simplify the complex fraction?

• Addition

• Division by a constant

• Multiplication by the reciprocal

• Subtraction

What is the reciprocal of the fraction used in the simplification?

• one over cosine x

• sine x over cosine x

• cosine x over sine x

• one over sine x

Which common factors are canceled out in the simplification process?

• cosine x and tangent x

• sine x and cosine x

• sine x and one plus cosine x

• tangent x and secant x

What remains after canceling out the common factors?

• secant x

• tangent x

• cosine x

• sine x

What is the final simplified form of the given expression?

• sine x

• cosine x

• tangent x

• secant x

What is the purpose of simplifying the given trigonometric expression?

• To add more terms

• To change the variable

• To make it more complex

• To find a simpler equivalent expression