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Question

If A+B+C=π, thencosAsinBsinC+cosBsinCsinA+cosCsinAsinB=1. If this is true enter 1, else enter 0.

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Solution

A+B+C=π
cosAsinBsinC+cosBsinCsinA+cosCsinAsinB
=cosAsinBsinC+sinAcosBsinC+sinasinBcosCsinAsinBsinC
=cosAcosBcosCcos(A+B+C)sinAsinBsinC=cosAcosBcosC+1sinAsinBsinC=cotAcotBcotC+cscAcscBcscC

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