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Question

The determinant ∣∣ ∣∣sinAcosAsinA+cosBsinBcosAsinB+cosBsinCcosAsinC+cosB∣∣ ∣∣ is equal to

A
0
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B
1
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C
sin2A+cosA
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D
sinA+cosB+cosA
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Solution

The correct option is A 0

∣ ∣sinAcosAsinA+cosBsinBcosAsinB+cosBsinCcosAsinC+cosB∣ ∣=∣ ∣sinAcosAsinAsinBcosAsinBsinCcosAsinC∣ ∣+∣ ∣sinAcosAcosBsinBcosAcosBsinCcosAcosB∣ ∣ Taking cosA,cosB common from C2,C3 respectively from second determinant=0+cosAcosB∣ ∣sinA11sinB11sinC11∣ ∣{C1,C3 and C2,C3 are same in first and second determinants respectively}=0+0


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