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ही * कला VIV¢ 2ण 29 सिद्ध कीजिए: ८०५९. + ८057 [+डोन [डे % दर

Answer»

We know, cos(90 + ø) = sinø cos²x = (1 + sin2x)/2

Now, (1 + cos2x)/2 + [1 + cos(2x + 2π/3 )]/2 + [ 1 + cos(2x - 2π/3)]/2 = 1/2 [ 1 + cos2x + 1 + cos(2x + 2π/3) + 1 + cos(2x -2π/3)] = 1/2[3 + cos2x + cos(2x +2π/3) + cos(2x - 2π/3)] = 1/2[ 3 + cos2x + (2cos(2x) × cos120] = 1/2[3 + cos2x + 2cos2X × cos(120) ] = 1/2[3 + cos2X + 2cos2X × cos(90 + 30) ] = 1/2[3 + cos2X + 2cos2X × (-sin30)] = 1/2[3 + cos2X + 2cos2X × (-1/2)] = 1/2[ 3 + cos2X - cos2x] 3/2

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