How do you prove cos(-a) = cos(360°-a) = cosa?

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Answer 1 · 2018-04-18T02:27:34

As proved.

![https://socratic.org/questions/in-which-quadrants-do-cosine-and-tangent-have-the-opposite-sign]( useruploads.socratic.org )

$cos (-a)$

From the above sign table,

$"Since 4 quadrants together form " 360^@$ ,

$cos -(a) = cos (360 + (-a)) = cos (360-a)$ .

$cos (360 -a) color(crimson)(" falls in IV Quadrant"$

$Also, cos (-a) = cos a, color(brown)(" as cos is +ve in I & IV Quadrants"$

Hence $cos (-a) = cos (360 - a) = cos a$