Trigonometric Functions and Identities

The video tutorial explains how to simplify a trigonometric expression by finding a common denominator for two fractions, subtracting them, and then simplifying the result using trigonometric identities. The expression is further rewritten as a product of trigonometric functions, specifically tangent and secant, and presented in alphabetical order. The tutorial provides a step-by-step approach to understanding the process of simplifying trigonometric expressions.

What is the first step in simplifying a trigonometric expression with different denominators?

• Multiply the numerators by each other

• Find a common denominator

• Subtract the numerators

• Add the fractions directly

How do you obtain a common denominator for the fractions 1/(1+sin x) and 1/(1-sin x)?

• Multiply both fractions by 1

• Multiply the first fraction by (1-sin x) and the second by (1+sin x)

• Add (1+sin x) to both fractions

• Subtract (1-sin x) from both fractions

What is the result of subtracting the numerators after obtaining a common denominator?

• 2

• -2 sin x

• sin x

• 0

What is the product of the two denominators (1+sin x) and (1-sin x)?

• sin^2 x + 1

• 1 + sin^2 x

• sin^2 x - 1

• 1 - sin^2 x

Which identity helps in simplifying the denominator 1 - sin^2 x?

• 1 + cot^2 x = csc^2 x

• sin x = 1/csc x

• tan^2 x + 1 = sec^2 x

• sin^2 x + cos^2 x = 1

What is the simplified form of the expression -2 sin x / cos^2 x?

• -2 tan x sec x

• -2 sec x tan x

• -2 sin x cos x

• -2 cos x sin x

Why is it necessary to rewrite the expression in alphabetical order?

• To match the textbook format

• To follow the instructions given

• To simplify the calculation

• To make it easier to read

What is the equivalent of sin x / cos x in trigonometric terms?

• csc x

• cot x

• tan x

• sec x

What is the equivalent of 1 / cos x in trigonometric terms?

• sin x

• cot x

• sec x

• tan x

What is the final expression after arranging the trigonometric functions in alphabetical order?

• -2 sec x tan x

• -2 tan x sec x

• -2 cos x sin x

• -2 sin x cos x