What is the general solution for sqrt(3)sin(x)=cos(x),-pi<= x<= pi ?

The general solution for sqrt(3)sin(x)=cos(x),-pi<= x<= pi is x= pi/6 ,x=-(5pi)/6

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sqrt(3)sin(x)=cos(x),-pi<= x<= pi

3 sin (x) = cos (x), - π \leq x \leq π

x = \frac{π}{6}, x = - \frac{5 π}{6}

Degrees

x = 3 0^{\circ}, x = - 15 0^{\circ}

Solution steps

3 sin (x) = cos (x), - π \leq x \leq π

Rewrite using trig identities

3 sin (x) = cos (x)

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{3 sin ( x )}{cos ( x )} = \frac{cos ( x )}{cos ( x )}

Simplify

\frac{3 sin ( x )}{cos ( x )} = 1

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

3 tan (x) = 1

3 tan (x) = 1

Divide both sides by

3

3 tan (x) = 1

Divide both sides by

3

\frac{3 tan ( x )}{3} = \frac{1}{3}

Simplify

\frac{3 tan ( x )}{3} = \frac{1}{3}

Simplify

\frac{3 tan ( x )}{3} : tan (x)

\frac{3 tan ( x )}{3}

Cancel the common factor:

3

= tan (x)

Simplify

\frac{1}{3} : \frac{3}{3}

\frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{3}{3}

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3}

General solutions for

tan (x) = \frac{3}{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}{6} + πn

x = \frac{π}{6} + πn

Solutions for the range

- π \leq x \leq π

x = \frac{π}{6}, x = - \frac{5 π}{6}

cos (x) = \frac{1999}{2000}

tan (13 5^{\circ} + x) = \frac{tan ( x ) - 1}{tan ( x ) + 1}

5 tan (x) + 5 = 0

sinh (x) = \frac{36}{77}

16 cos (θ) = 4

What is the general solution for sqrt(3)sin(x)=cos(x),-pi<= x<= pi ?
The general solution for sqrt(3)sin(x)=cos(x),-pi<= x<= pi is x= pi/6 ,x=-(5pi)/6