Question #e5c29

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Answer 1 · 2017-08-11T07:31:55

$\frac{1}{\sqrt{2}}$ $1/sqrt(2)$

$tan x + cot x = 2$ $tanx + cotx = 2$

$tan x + \frac{1}{tan x} = 2$ $tanx + 1/tanx = 2$

$\frac{{tan}^{2} x}{tan x} + \frac{1}{tan x} = 2$ $tan^2x/(tanx) + 1/tanx = 2$

$\frac{{tan}^{2} x + 1}{tan x} = 2$ $(tan^2x + 1)/(tanx) = 2$

${tan}^{2} x + 1 = 2 tan x$ $tan^2x + 1 = 2tanx$

${tan}^{2} x - 2 tan x + 1 = 0$ $tan^2x - 2tanx + 1 = 0$

let $a = tan x$ $a = tanx$

$a^{2} - 2 a + 1 = 0$ $a^2 - 2a + 1 = 0$

${(a - 1)}^{2} = 0$ $(a-1)^2 = 0$

$a - 1 = 0$ $a - 1 = 0$

$tan x - 1 = 0$ $tanx - 1 = 0$

$tan x = 1$ $tanx = 1$

$x = {tan}^{- 1} (1)$ $x = tan^-1(1)$

$x = 45$ $x = 45$ degrees.

$sin x$ $sinx$

$= sin 45$ $= sin45$

$= \frac{1}{\sqrt{2}}$ $= 1/sqrt(2)$