सिद्ध कीजिए कि - ` cos^(2) A+ cos^(2) (A + pi/3) + cos^(2) (A - pi/3) = 3/2`

Explanation

` L.H.S = cos^(2) A +cos^(2) (A+pi/3)+ cos^(2) (A= pi/3) `
` = 1/2 [ 2 cos^(2) A+2 cos^(2) (A+ 60^(@))+2 cos^(2) (A-60^(@))]`
` = 1/2 [ 1 + cos 2 A + 1 + cos ( 2A + 120 ^(@))`
` + 1 + cos (2A - 120^(@))] `
` = 1/2 [ 3 + cos 2A + cos (2A +120^(@) ) +cos (2A - 120^(@))] `
` = 1/2 [ 3 + cos 2A + 2cos. (2A+ 120^(2) + 2A - 120^(@))/2`
` cos. (2A +120^(@) - 2A +120^(@))/2 ]`
` = 1/2 [ 3 + cos 2A + 2 cos 2 A cos 120^(@)] `
` = 1/2 [ 3+ cos 2A + 2 cos 2A cos (90^(@)+ 30^(@))] `
` = 1/2 [ 3 + cos 2A - 2 cos 2A sin 30^(@) ] `
` = 1/2 [ 3+ cos 2A - 2 * cos 2A * (1/2)]`
` = 1/2 (3+ cos 2A - cos 2A)= 3/2 = R.H.S `