Question

Prove that, Cos20°+Cos100°+Cos140°== 0

Answer 1

We know
$\cos( \alpha ) + \cos( \beta ) = 2 \cos( \frac{ \alpha + \beta }{2} ) \cos( \frac{ \alpha - \beta }{2} )$
Therefore
cos 20 + cos 100 = 2.cos 60 cos 40
= 2. (1/2).cos 40
= cos 40
Hence cos 20 + cos 100 + cos 140 =
cos 40 + cos 140 =
2.cos 90 cos 50 = 2.0.cos 50 = 0
Hope this helps.