21) In a
triangle ABC, if sin A sinB sinC=1/3 then the value of cotAcotB+cotB cot C+cot C cot A is.
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Step-by-step explanation:
A+B+C=180
A+ B=180 -C
Taking tan on both sides,
tan(A+B)=tan(180 -C)
tanA +tanB/1 - tanAtanB = -tanC. ( using identity)
tanA + tanB = -tanC(1- tanA.tanB)
tanA + tanB= -tanC + tanCtanBtanC
tanA + tanB + tanC = tanAtanBtanC
Divide by tanA.tanB.tanC
we get,
cotBcotC + cotAcotC + cotAcotB = 1
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