Question

cos 52 + cos 68 + cos172 = 0 ... prove​

Answer 1

Step-by-step explanation:

$\cos( \alpha) + \cos ( \beta ) = 2 \cos( \frac{ \alpha + \beta }{2} ) \cos( \frac{ \alpha - \beta }{2} )$

So cos(52°)+ cos(68°) =>

2 cos(52+68)/2cos(52-68)/2 =>

2cos(60°)cos(-8°) =>2×1/2×cos(8°) =>cos(8°). Note that cos(-x) =>cos(x).

cos(8°)+cos(172°) =>

2cos(8+172)/2cos(8-172)/2 =>

2cos(90°)cos(-82°) =>2×0×cos(82°) =>0. Hence proved. Hope it helps you.