Question

Derive a formula for cos(2????) in terms of sin(????) and cos(????) for all real numbers u

Answer 1

Answer: (2α) = cos²(α) - sin²(α)

Explanation:

The expression for cosine of the sum of two angles is:

cos (α + β) = cos(α)*cos(β) - sin(α)*sin(β)

in case α = β

cos ( α + α ) = cos (2α) = cos(α)*cos(α) - sin(α)*cos(α)

Hence cos (2α) = cos²(α) - sin²(α)