Question

cos(30°-A) +cos(30°+A) =√3 cos A

Answer 1

Here is your answer mate
LHS
=cos (30-A)+cos(30+A)

As cos(x+y)+cos (x-y)=2cos(x+y)/2 *cos(x-y)/2

=2cos (30-A+30+A)/2 *cos(30-A-(30+A))/2

=2(cos (30-A+30+A)/2 )*cos(30-A-30-A)/2

= 2cos30*cos (-A)

=2cos 30*cosA

because cos(-x)=cos x

=2*root3/2*cos A

=root 3 cosA

Hope this helps.

Answer 2

L.H.S- cos(30°-A)+cos(30°+A)=√3 cos A

=2cos(30°-A+30°+A)/2.cos[30°-A-(30°+A)] [•°• cosC+cosD=2cosC+D/2 cosC-D/2]

=2cos60°/2 cos-2A/2

=2cos30°cos-A

=2.√3/2 cosA[•°•cos30°=√3/2, cos(-x)=cosC

=√3cosA

HENCE PROVED...