cot(x+y) = (cotxcoty-1)/(cotx+coty)?
How can I prove the identity cot(x+y) = (cot x cot y - 1) / (cot x + cot y)? I would really appreciate your help!
3 Answers
Feb 04, 2025
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
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