What is the general solution for tan^2(x)-3=0,0<x< pi/2 ?

Q: What is the general solution for tan^2(x)-3=0,0<x< pi/2 ?

The general solution for tan^2(x)-3=0,0<x< pi/2 is x= pi/3

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Popular >

tan^2(x)-3=0,0<x< pi/2

Solution

tan^{2} (x) - 3 = 0, 0 < x < \frac{π}{2}

Solution

x = \frac{π}{3}

Degrees

x = 6 0^{\circ}

Solution steps

tan^{2} (x) - 3 = 0, 0 < x < \frac{π}{2}

Solve by substitution

tan^{2} (x) - 3 = 0

Let:

tan (x) = u

u^{2} - 3 = 0

u^{2} - 3 = 0 : u = 3, u = - 3

u^{2} - 3 = 0

Move

3

to the right side

u^{2} - 3 = 0

Add

3

to both sides

u^{2} - 3 + 3 = 0 + 3

Simplify

u^{2} = 3

u^{2} = 3

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = 3, u = - 3

Substitute back

u = tan (x)

tan (x) = 3, tan (x) = - 3

tan (x) = 3, tan (x) = - 3

tan (x) = 3, 0 < x < \frac{π}{2} : x = \frac{π}{3}

tan (x) = 3, 0 < x < \frac{π}{2}

General solutions for

tan (x) = 3

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{3} + πn

x = \frac{π}{3} + πn

Solutions for the range

0 < x < \frac{π}{2}

x = \frac{π}{3}

tan (x) = - 3, 0 < x < \frac{π}{2} :

No Solution

tan (x) = - 3, 0 < x < \frac{π}{2}

General solutions for

tan (x) = - 3

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{2 π}{3} + πn

x = \frac{2 π}{3} + πn

Solutions for the range

0 < x < \frac{π}{2}

No Solution

Combine all the solutions

x = \frac{π}{3}

Popular Examples

3cot^2(x)=7csc(x)-7

3 cot^{2} (x) = 7 csc (x) - 7

sin(x)=0.86

sin (x) = 0.86

2sin(2θ)+sqrt(3)=0

2 sin (2 θ) + 3 = 0

sin^2(x)+4sin(x)+3=0

sin^{2} (x) + 4 sin (x) + 3 = 0

cos^2(x)-sin^2(x)=(sqrt(2))/2

cos^{2} (x) - sin^{2} (x) = \frac{2}{2}

Frequently Asked Questions (FAQ)

What is the general solution for tan^2(x)-3=0,0<x< pi/2 ?
The general solution for tan^2(x)-3=0,0<x< pi/2 is x= pi/3