Question #18b64

1 Answer
Nghi N.
Mar 18, 2017

13.23

Explanation:

tan x + 1/tan x = 2
tan^2 x + 1 = 2tan x
tan^2 x - 2tan x + 1 = 0
Solve this quadratic equation for tan x.
Since a+ b + c = 0, use shortcut. There are 2 real roots:
tan x = 1 and tan x = c/a = 1/2.
a. tan x = 1 --> x = pi/4
10x --> (10pi)/4 --> (5pi)/2 --> pi/2
tan 10x + cot 10x = tan (pi/2) + cot (pi/2) = Inf. + 0 = Infinity (rejected)
b. tan x = 1/2 --> x = 26^@565
10x = 265^@65
tan 10x + cot 10x = tan (265.65) + cot (265.65) =
= 13.15 + 0.08 = 13.23

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