Question

$\cos(24) + \cos(55) + \cos(55) + \cos(204) + \cos(300 \\)$
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Answer 1

L.H.S. = cos24+cos204+cos55 + cos125 +cos300

= cos 24 + cos (180+24) + sin (90-55) + cos (90+35) + cos (360-60) [ cos x = sin (90-x)]

= cos 24 - cos 24 + sin 35 - sin 35 + cos 60 [ cos (180 + x ) = - cosx ; cos (90 + y ) = - sin y ; cos (360 - x ) = cos x ]

= (cos 24 - cos 24) + (sin 35 - sin 35 )+ cos 60

= 0 + 0 + 1/2 = 1/2 = R.H.S.