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

Answer: (2α) = cos² (α) - sin² (α)

Step-by-step 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)