Question

Convert all of these into a product:

NUMBER 1: √3 +2 cos(α)
NUMBER 2: sin(α− 2π/3 )− sin(α+ 2π/3 )
NUMBER 3: cos(2α− π/16)+ cos( 9π/16−2α)
NUMBER 4: 4 sin²α−3

Answer 1

To convert the given expressions into a product, we simplify them using trigonometric identities, resulting in products of trigonometric functions.

Step-by-step explanation:

To convert the given expressions into a product, we need to simplify them using trigonometric identities.

1. NUMBER 1: √3 +2 cos(α) = √3 + 2 cos(α)
2. NUMBER 2: sin(α− 2π/3 )− sin(α+ 2π/3 ) = 2 sin(π/3) cos(α) - 2 cos(π/3) sin(α)
3. NUMBER 3: cos(2α− π/16) + cos(9π/16− 2α) = 2 cos(4π/16 - α) cos(5π/16 - α)
4. NUMBER 4: 4 sin²α−3 = 4 sinα sinα - 3

By using trigonometric identities and simplifying the expressions, we have transformed each of them into a product of trigonometric functions.