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trapecia [35]
3 years ago
12

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

Mathematics
2 answers:
Wewaii [24]3 years ago
8 0

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)

iragen [17]3 years ago
8 0

Answer:

x = 30 or x = 210

Step-by-step explanation:

Given equation is:

\[\tan x - \sqrt{1 - 2*\tan ^{2} x} = 0\]&#10;

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

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