Question

Question #18b64

Answer 1

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`