Double Angle Formulas - Practice Questions & MCQ

Double Angle Formula and Reduction Formula

Proof:

The double-angle formulas are a special case of the sum formulas, where α = β.

For sine

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

    If we let α = β = θ, then we have

    sin(θ + θ) = sin θ cos θ + cos θ sin θ

    sin(2θ) = 2 sin θ cos θ 

For cosine

cos(α + β) = cos α cos β − sin α sin β,

Letting α = β = θ, we have

cos(θ + θ) = cos θ cos θ − sin θ sin θ

cos(2θ) = cos² θ − sin² θ

We can write this formula in different forms as per the requirement of the question,

The second variation is:

For tan

Replacing α = β = θ in the sum formula gives

Reduction Formula

The double-angle formulas can be used to derive the reduction formulas, which are formulas we can use to reduce the power of a given expression involving even powers of sine or cosine.