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Simplify: cot (Ⱦ-γ) cot (γ-Ƚ) +cot (γ-Ƚ) cot (Ƚ-Ⱦ) + cot (Ƚ-Ⱦ) cot (Ⱦ-γ)

Simplify: cot (Ⱦ-γ) cot (γ-Ƚ) +cot (γ-Ƚ) cot (Ƚ-Ⱦ) + cot (Ƚ-Ⱦ) cot (Ⱦ-γ) 

Grade:11

1 Answers

Aditya Gupta
2075 Points
2 years ago
let A=x-y
B=y-z
C=z-x
so all we gotta do now is to find the value cotAcotB+cotBcotC+cotCcotA
This is equal to (tanA+tanB+tanC)/tanAtanBtanC
Note that A+B+C=0
so, tan(A+B+C)=(tanA+tanB+tanC-tanAtanBtanC)/(1 – tanAtanB – tanBtanC – tanCtanA)=0
or, tanA+tanB+tanC=tanAtanBtanC
so, the answer is (tanA+tanB+tanC)/tanAtanBtanC = 1 (one)

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