Question

Prove That ??? Cos306°+Cos234°+cos162°+Cos18° = 0

Answer 1

see below

Explanation:

`cos306" is in Q.IV ":. cos306=+cos(360-306)=cos54`

`cos234" is in Q.III":.cos234=-cos(234-180)=-cos54`

`cos162" is in Q>II":.cos162=-cos(180-162)=-cos18`

`cos306+cos234+cos162+cos18`

`=cos54-cos54-cos18+cos18=0`

Answer 2

Please see the explanation below

Explanation:

Let's transform the angles

according to the trigonometric circle

`cos(306)=cos(360-306)=cos54`

`cos(234)=-cos(234-180)=-cos54`

`cos162=-cos(180-162)=-cos18`

Therefore,

`cos306+cos234+cos162+cos18`

`=cos54-cos54-cos18+cos18`

`=0`