Question

Solve tan x - square root 1-2tan^2x=0 given that 0 degrees < x<360degrees

Answer 1

Answer:

x=30° or 210°

Step-by-step explanation:

The given equation is:

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

Taking the second term to RHS we get

$tanx=\sqrt{1-2tan^{2}x }$

Squaring both sides of the equation,we get

$tan^{2}x=1-2tan^{2}x$

$3tan^{2}x=1$

$tan^{2}x=\frac{1}{3}$

∴tanx=±$\frac{1}{\sqrt{3} }$

But tanx cannot be negative as RHS in the given equation will be positive always. Hence tanx=$\frac{1}{\sqrt{3} }$

∴ x=30° or x=180°+30°=210° (As tan is positive in first and third quadrant)

Answer 2

Answer:

x = 30 or x = 210

Step-by-step explanation:

Given equation is:

$\[\tan x - \sqrt{1 - 2*\tan ^{2} x} = 0\]$

Simplifying,

$\[\tan x = \sqrt{1 - 2*\tan ^{2} x}\]$

Squaring both sides,

$\[\tan ^{2} x = 1 - 2*\tan ^{2} x\]$

=> $\[\tan ^{2} x + 2*\tan ^{2} x = 1\]$

=> $\[\3*\tan ^{2} x= 1\]$

=> $\[\tan x= \pm \frac{1}{\sqrt{3}}\]$

Solving for x which satisfies the above equality and also 0 < x < 360,

x = 30 or x = 210