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How do I solve for the equation 0 ≤ x < 2π √2 tan x = 2 sin x ?

1 Answer

Feb 22, 2018

$x = \frac{π}{4}, \frac{7}{4} π$ $x = pi/4, 7/4 pi$

Explanation:

$\sqrt{2} tan x = 2 sin$ $sqrt(2) tan x = 2 sin$

$\frac{tan x}{sin x} = \frac{2}{\sqrt{2}}$ $tan x / sin x = 2/ sqrt(2)$

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

note:
$tan x /sin x = tan x -: sin x = sin x/cos x -: sin x = cancel(sin x)/cos x * 1/ cancel(sin x) = 1/cos x$

$cos x = 1/sqrt (2)$

$x = pi/4, 7/4 pi$

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