Simplify 24 Trigonometric Expressions With Identities

Which identity is used to express tangent in terms of sine and cosine?

• Cofunction Identity

• Pythagorean Identity

• Quotient Identity

• Reciprocal Identity

What is the result of simplifying the expression tan(x) * csc(x)?

• sin(x)

• 1

• cot(x)

• sec(x)

How can you simplify an expression involving sec^4(x) - tan^4(x)?

• Use the difference of squares

• Convert to sine and cosine

• Apply the even-odd identity

• Use the cofunction identity

What is the first step in simplifying a fraction like csc(θ) / sec(θ)?

• Use the Pythagorean identity

• Add the numerators

• Multiply by the reciprocal

• Factor the denominator

When simplifying 1 - sin^2(x), what identity is used?

• Cofunction Identity

• Reciprocal Identity

• Quotient Identity

• Pythagorean Identity

What is the result of multiplying the conjugate in the expression (csc(x) + 1) / (csc(x) - 1)?

• Simplifies to zero

• Creates a Pythagorean identity

• Results in a complex fraction

• Converts to sine and cosine

Which identity helps in simplifying expressions like cos(π/2 - x)?

• Even-Odd Identity

• Cofunction Identity

• Quotient Identity

• Reciprocal Identity

What is the simplified form of cos(x) / sin(x) + sin(x) / cos(x)?

• 1

• sec(x) * csc(x)

• tan(x) + cot(x)

• sin^2(x) + cos^2(x)

How do you simplify an expression with a common denominator like (cos^2(x) + sin^2(x)) / (cos(x) * sin(x))?

• Use the Pythagorean identity

• Multiply by the conjugate

• Factor the numerator

• Apply the even-odd identity

What is the result of applying the even-odd identity to sin(-x) * cos(x)?

• sin(x) * cos(x)

• -cos(x) * sin(x)

• -sin(x) * cos(x)

• cos(x) * sin(x)