The correct option is D
The required solution is x= 5π/3
Since,
sin(x+ startfraction pi over 2 endfraction) = 1/2
Thus,
cos x= 1/2
cos x = cosπ/3 or cos (2π-π/3)
cos x= cos 5π/3, since x∈ [3π/2, 2π]
The question is a little incorrect, the correct question is
Solve: sin (x + StartFraction pi Over 2 EndFraction) = one-half for left-bracket StartFraction 3 pi Over 2 EndFraction, 2 pi right-bracket.
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