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Question

In a triangle ABC, the value of the determinant ∣ ∣ ∣ ∣sinA2sinB2sinc2sin(A+B+C)sinB2cosA2cos(A+B+C2)tan(A+B+C)sinC2∣ ∣ ∣ ∣ is less than or equal to

A
12
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B
14
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C
18
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D
None of these
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Solution

The correct option is C 18
Let Δ=∣ ∣ ∣ ∣sinA2sinB2sinc2sin(A+B+C)sinB2cosA2cos(A+B+C2)tan(A+B+C)sinC2∣ ∣ ∣ ∣=∣ ∣ ∣ ∣sinA2sinB2sinc20sinB2cosA200sinC2∣ ∣ ∣ ∣=sinA2sinB2sinC2
but sinA2sinB2sinC218Δ18

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