Answer:
x=30° or 210°
Step-by-step explanation:
The given equation is:
[tex]tanx-\sqrt{1-2tan^{2}x}=0[/tex]
Taking the second term to RHS we get
[tex]tanx=\sqrt{1-2tan^{2}x }[/tex]
Squaring both sides of the equation,we get
[tex]tan^{2}x=1-2tan^{2}x[/tex]
[tex]3tan^{2}x=1[/tex]
[tex]tan^{2}x=\frac{1}{3}[/tex]
∴tanx=±[tex]\frac{1}{\sqrt{3} }[/tex]
But tanx cannot be negative as RHS in the given equation will be positive always. Hence tanx=[tex]\frac{1}{\sqrt{3} }[/tex]
∴ x=30° or x=180°+30°=210° (As tan is positive in first and third quadrant)
Answer:
x = 30 or x = 210
Step-by-step explanation:
Given equation is:
[tex]\[\tan x - \sqrt{1 - 2*\tan ^{2} x} = 0\] [/tex]
Simplifying,
[tex]\[\tan x = \sqrt{1 - 2*\tan ^{2} x}\][/tex]
Squaring both sides,
[tex]\[\tan ^{2} x = 1 - 2*\tan ^{2} x\][/tex]
=> [tex]\[\tan ^{2} x + 2*\tan ^{2} x = 1\][/tex]
=> [tex]\[\3*\tan ^{2} x= 1\][/tex]
=> [tex]\[\tan x= \pm \frac{1}{\sqrt{3}}\][/tex]
Solving for x which satisfies the above equality and also 0 < x < 360,
x = 30 or x = 210
