Asked by Tan
Find all angles between 0 and 2 phi inclusive which satisfy
cot 2z = 1 + cot z
cot 2z = 1 + cot z
Answers
Answered by
oobleck
that's <u>pi</u>, not phi
cot 2z = 1 + cotz
(cot^2 z - 1)/(2cotz) = 1+cotz
cot^2z - 1 = 2cotz + 2cot^2z
cot^2z + 2cotz + 1 = 0
(cotz+1)^2 = 0
cotz = -1
z = 3π/4, 7π/4
all solutions are nπ - π/4
cot 2z = 1 + cotz
(cot^2 z - 1)/(2cotz) = 1+cotz
cot^2z - 1 = 2cotz + 2cot^2z
cot^2z + 2cotz + 1 = 0
(cotz+1)^2 = 0
cotz = -1
z = 3π/4, 7π/4
all solutions are nπ - π/4
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