5.5 Double-Angle Identities

Double-Angle Identities

Proofs:

Verify

Note: From the double angle formula for cos(2A), the following can be derived which are very useful in Calculus.

Example

Given and cos θ < 0, find sin 2θ, cos 2θ, and tan 2θ.

Example

Find the values of the six trig function of θ if .

Hint: Begin with double angle formula for cos 2θ to find sin θ and cos θ

Example

Verify that the following equation is an identity.

Example

Simplify each expression: Ans: a) cos 10x b) -¼

a) b)

Example

Write cos 3x in terms of cos x.

Product-To-Sum Identities

Again – these are useful for rename for integration in Calculus

Example

Write as the sum or difference of two functions.

Sum-To-Product Identities

Example

Write as a product of two functions.