Question: "How to derive trig identity from the common..." - Plainmath

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Brock Brown

Answered question

2021-12-06

How to derive trig identity from the common ones?
$\cos^{2} x = \frac{1 + \cos 2 x}{2}$

Answer & Explanation

Papilys3q

Beginner2021-12-07Added 34 answers

Just use the double angle formula for

\cos 2 x

\cos 2 x = \cos^{2} x - \sin^{2} x - (1 - \cos^{2} x) = 2 \cos^{2} x - 1 r i g h t \Rightarrow \cos^{2} x = \frac{1 + \cos 2 x}{2}

And

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

, where

α = β

Ella Williams

Beginner2021-12-08Added 28 answers

e^{2 i x} = e^{i x} \times e^{i x} = {(\cos x + i \sin x)}^{2} = \cos^{2} x - \sin^{2} x + 2 i \cos x \sin x

\cos^{2} x + \sin^{2} x = - 1

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