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If $A + B + C = π / 2$ , then $\sin^{2} A + \sin^{2} B + \sin^{2} C + 2 \sin A \sin B \sin C$ is equal to

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Correct option is B

sin2⁡A+sin2⁡B+sin2⁡C+2sin⁡Asin⁡Bsin⁡C=1−cos2⁡A−sin2⁡B+sin⁡C[sin⁡C+2sin⁡Asin⁡B]=1−cos⁡(A+B)cos⁡(A−B)+sin⁡C[cos⁡(A+B) +2sin⁡Asin⁡B] [∵C=π/2−A−B]=1−cos⁡(π/2−C)cos⁡(A−B)+sin⁡Ccos⁡(A−B)=1

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