Hyperbolic Functions and Identities

This video tutorial focuses on verifying various hyperbolic identities, including hyperbolic cosine plus sine, cosine minus sine, and double angle formulas for hyperbolic sine and cosine. It also covers the verification of negative hyperbolic sine identity and hyperbolic tangent and secant identities. The tutorial emphasizes the use of exponential forms and sum and difference formulas to prove these identities.

What is the exponential form of hyperbolic cosine?

• e^x / e^(-x)

• e^x * e^(-x) / 2

• e^x + e^(-x) / 2

• e^x - e^(-x) / 2

How do you simplify the expression e^x + e^(-x) - e^x + e^(-x)?

• 2e^x

• e^x - e^(-x)

• 0

• 2e^(-x)

Which formula is used to verify the double angle formula for hyperbolic sine?

• Sum and difference formulas

• Pythagorean identities

• Quotient identities

• Reciprocal identities

What is the result of hyperbolic sine of 2x?

• cosh(x) - sinh(x)

• sinh^2(x) + cosh^2(x)

• 2 * sinh(x) * cosh(x)

• sinh(x) * cosh(x)

What is the identity for hyperbolic sine of negative x?

• -sinh(x)

• cosh(x)

• sinh(x)

• -cosh(x)

What is the double angle formula for hyperbolic cosine?

• cosh^2(x) + sinh^2(x)

• 2 * cosh(x) * sinh(x)

• cosh^2(x) - sinh^2(x)

• sinh^2(x) - cosh^2(x)

What is the identity for 1 - tanh^2(x)?

• coth^2(x)

• sinh^2(x)

• csch^2(x)

• sech^2(x)

How do you express hyperbolic tangent in terms of hyperbolic sine and cosine?

• cosh(x) / sinh(x)

• sinh(x) / cosh(x)

• 1 / sinh(x)

• 1 / cosh(x)

What is the result of dividing e^x by e^(-x)?

• 1

• e^(-2x)

• e^0

• e^(2x)

What is the identity for hyperbolic secant squared?

• 1 / cosh^2(x)

• cosh^2(x) - sinh^2(x)

• 1 / sinh^2(x)

• sinh^2(x) + cosh^2(x)