Does $cos 240 = {(cos 120)}^{2} - {(sin 120)}^{2}$ $cos240=(cos120)^2-(sin120)^2$ ?

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Answer 1 · 2016-10-21T23:48:33

Oct 21, 2016

Yes

Answer 2 · 2016-10-22T02:37:21

Yes, it does

A common trigonometric identity states that

$cos (2 θ) = {cos}^{2} (θ) - {sin}^{2} (θ)$ $cos(2theta) = cos^2(theta) - sin^2(theta)$ for any angle $θ$ $theta$ .

This can be derived from the sum of angles formula

$cos (α + β) = cos (α) cos (β) - sin (α) sin (β)$ $cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)$

by setting $α = β$ $alpha = beta$ .

In the given case, that gives us

${cos}^{2} (120) - {sin}^{2} (120) = cos (2 \cdot 120) = cos (240)$ $cos^2(120) - sin^2(120) = cos(2*120) = cos(240)$

Does cos240=(cos120)^2-(sin120)^2cos240=(cos120)2−(sin120)2cos240=(cos120)^2-(sin120)^2?