How do you solve 2cotx-4/cotx=7 in the interval 0<=x<=2pi?

1 Answer
Nghi N
Jun 14, 2017

14^@04; -63^@43

Explanation:

2cot x - 4/(cot x) - 7 = 0
2cot^2 x - 7cot x - 4 = 0
Solve this quadratic equation for cot x.
D = d^2 = b^2 - 4ac = 49 + 32 = 81 --> d = +- 9
There are 2 real roots:
cot x = -b/(2a) +- d/(2a) = 7/4 +- 9/4
a. cot x = 16/4 = 4 --> tan x = 1/4
Calculator gives -->
x = 14^@04
b. cot x = -2/4 = -1/2 --> tan x = - 2
x = -63^@43

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