Master Verifying a trigonometric identity

The video tutorial explains how to verify trigonometric identities by equating both sides of an equation. It emphasizes choosing the more complex side to simplify using trigonometric identities like Pythagorean, even/odd, and rewriting in terms of sines and cosines. Several examples demonstrate the process, including using secant, cosine, sine, and cotangent, highlighting different strategies and common pitfalls.

What is the primary goal when verifying a trigonometric identity?

• To convert all terms to sines and cosines

• To simplify the expression to a single trigonometric function

• To prove that both sides of the equation are equal

• To find the value of the variable

When simplifying a trigonometric identity, which side should you typically start with?

• The side with a numerical value

• The side with more complex expressions

• The side with fewer terms

• The side with only one trigonometric function

Which identity is used to simplify expressions involving secant and cosine?

• Pythagorean identity

• Quotient identity

• Reciprocal identity

• Even-odd identity

What is the result of multiplying (1 + sin(θ))(1 - sin(θ))?

• tan(θ)

• 1

• cos²(θ)

• sin²(θ)

How do you verify an identity involving cotangent and sine?

• Convert to tangent and cosine

• Use the Pythagorean identity

• Rewrite in terms of sines and cosines

• Apply the even-odd identity

What should you do when faced with multiple trigonometric terms in an identity?

• Rewrite each term in terms of sines and cosines

• Use only the Pythagorean identities

• Simplify using numerical values

• Convert all terms to tangent

In the example involving cosine squared and sine squared, what is the key step to verify the identity?

• Apply the distributive property

• Use the reciprocal identity

• Combine like terms

• Convert to tangent