cot(x+y) = (cotxcoty-1)/(cotx+coty)?

how to prove it?

plz help me!!

3 Answers

  • cot(x+y) = (cotxcoty-1)/(cotx+coty)?

    Girl, please read patiently. It is NOT tough but needs patience.

    LHS = cot(x+y)

    = cos(x+y) / sin(x+y)

    = [(cosxcosy - sinxsiny) / (sinxcosy + cosxsiny)]

    Divide numerator and denominator by sinx*siny, we get

    (cotxcoty-1)/(coty+cotx),

    = (cotxcoty-1)/(cotx+coty) = RHS

  • Y Cot X

  • cot (x+y) = 1 / tan (x+y) = 1/ [(tan x + tan y)/(1 - tan x tan y)] = (1 - tan x tan y) / (tan x + tan y) = (1 - (1/(cot x cot y))) / (1/cot x + 1/cot y) = ((cot x cot y - 1)/(cot x cot y)) / ((cot x + cot y)/(cot x cot y)) = (cot x cot y - 1) / (cot x + cot y) Proved !!!

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