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Question

If A,B and C denote the angles of a triangle,
then =∣ ∣1cosCcosBcosC1cosAcosBcosA2∣ ∣ independent of

A
A
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B
B
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C
C
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D
None of these
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Solution

The correct option is D B
Multiplying C1 by a and then applying
C1C2+bC2+CC3 we get
Δ=1a∣ ∣a+bcosC+ccosBcosCcosBacosCbccosA1cosAacosB+bcosA2ccosA2∣ ∣
Δ=1a∣ ∣0cosCcosB01cosAccosA2∣ ∣
Δ=ca(cosCcosA+cosB)
Δ=casinCsinA, which is independent of B

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