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Question

If A,B,C(2n+1)π2, then the numerical value of sin(BC)cosBcosC+sin(CA)cosCcosA+sin(AB)cosAcosB is

A
1
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B
2
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C
0
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D
2
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Solution

The correct option is C 0
Here,
sin(BC)cosBcosC=sinBcosCcosBsinCcosBcosC=tanBtanC(1)

Similarly,
sin(CA)cosCcosA=tanCtanA(2)

sin(AB)cosAcosB=tanAtanB(3)

Adding the equations (1),(2) and (3), we get
sin(BC)cosBcosC+sin(CA)cosCcosA+sin(AB)cosAcosB=0

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