Does #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(2theta) = cos^2(theta) - sin^2(theta)# for any angle #theta#.

This can be derived from the sum of angles formula

#cos(alpha+beta)=cos(alpha)cos(beta)-sin(alpha)sin(beta)#

by setting #alpha = beta#.

In the given case, that gives us

#cos^2(120) - sin^2(120) = cos(2*120) = cos(240)#