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Question

Evaluate sin(CA)sinCsinA if none of sin A, sin B, sin C is zero.

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Solution

sin(CA)sinCsinA

=sinCcosAcosCsinAsinCsinA

=sinCcosAsinCsinAcosCsinAsinCsinA

=cosAsinAcosCsinC

=cotAcotC

=cotAcotC+cotCcotB+cotBcotA=0

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