Half angle formulas (Power reducing formulas)

Last updated at August 11, 2026 by

We know from double angle formula that

Double angle formulas.jpg

 

These identities can also be used to reduce angles

Half angle formulas (Power reducing formulas) - Part 2

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Transcript

We know from double angle formula that sin 2x = 2 sin x cos x = 2 tan x / (1 + tan^2 x) cos 2x = cos^2 x - sin^2 x = 1 - 2 sin^2 x = 2 cos^2 x - 1 = 1 - tan^2 x / 1 + tan^2 x tan 2x = 2 tan x / (1 - tan^2 x) These identities can also be used to reduce angles sin x = 2 sin x/2 cos x/2 = 2 tan x/2 / (1 + tan^2 x/2) cos x = cos^2 x/2 - sin^2 x/2 = 1 - 2 sin^2 x/2 = 2 cos^2 x/2 - 1 = 1 - tan^2 x/2 / 1 + tan^2 x/2 tan x = 2 tan x/2 / (1 - tan^2 x/2)

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