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If $π < α < \frac{3 π}{2},$ the the expression $\sqrt{4 \sin^{4} α + \sin^{2} 2 α} + 4 \cos^{2} (\frac{π}{4} - \frac{α}{2})$ is equal to

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2+4sin⁡α

2−4sin⁡α

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Correct option is C

We have,4sin4⁡α+sin2⁡2α+4cos2⁡π4−α2=4sin2⁡αsin2⁡α+cos2⁡α+41+cos⁡π2−α2=2|sin⁡α|+2(1+sin⁡α)=−2sin⁡α+2(1+sin⁡α)=2 ∵ sin⁡α<0] for α∈3π/2

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If π<α<3π2, the the expression 4sin4⁡α+sin2⁡2α+4cos2⁡π4−α2 is equal to

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If $π < α < \frac{3 π}{2},$ the the expression $\sqrt{4 \sin^{4} α + \sin^{2} 2 α} + 4 \cos^{2} (\frac{π}{4} - \frac{α}{2})$ is equal to