Trigonometric Identities and Simplifications

The video tutorial covers simplifying trigonometric expressions using fundamental identities. It begins with an introduction to the basic identity of cosine squared theta plus sine squared theta equals one. The tutorial then demonstrates simplifying expressions by substituting equivalent trigonometric identities. Examples include simplifying expressions like 1 minus sine squared theta times cosine squared theta and sine squared theta over 1 minus sine squared theta. The video concludes with an example of adding trigonometric functions and simplifying the result using known identities.

What is the fundamental trigonometric identity derived from the unit circle?

• sin^2(theta) - cos^2(theta) = 1

• tan^2(theta) + 1 = sec^2(theta)

• cos^2(theta) + sin^2(theta) = 1

• 1 + cot^2(theta) = csc^2(theta)

How can 1 - sin^2(theta) be expressed using a trigonometric identity?

• tan^2(theta)

• cos^2(theta)

• csc^2(theta)

• sec^2(theta)

What is the simplified form of 1 - sin^2(theta) * cos^2(theta)?

• sec^4(theta)

• tan^4(theta)

• sin^4(theta)

• cos^4(theta)

What is the equivalent expression for sin^2(theta) / (1 - sin^2(theta))?

• tan^2(theta)

• cot^2(theta)

• sec^2(theta)

• csc^2(theta)

How can sin^2(theta) / cos^2(theta) be expressed?

• csc^2(theta)

• sec^2(theta)

• cot^2(theta)

• tan^2(theta)

What is the simplified result of cos^2(theta) + 1 + sin^2(theta)?

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• 1

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Which identity helps in simplifying cos^2(theta) + sin^2(theta)?

• cos^2(theta) + sin^2(theta) = 1

• tan^2(theta) + 1 = sec^2(theta)

• sin^2(theta) - cos^2(theta) = 1

• 1 + cot^2(theta) = csc^2(theta)

What is the value of cos^2(theta) + sin^2(theta) for any angle theta?

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Which trigonometric identity is used to simplify expressions involving sin^2(theta) and cos^2(theta)?

• cos^2(theta) + sin^2(theta) = 1

• tan^2(theta) + 1 = sec^2(theta)

• 1 + cot^2(theta) = csc^2(theta)

• sin^2(theta) - cos^2(theta) = 1

What is the result of adding cos^2(theta) and sin^2(theta)?

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