Question

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.​

Answer 1

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

Answer 2

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