What is the general solution for 3/(sin(x))= 1/(cos(x)) ?

The general solution for 3/(sin(x))= 1/(cos(x)) is x=1.24904…+pin

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3/(sin(x))= 1/(cos(x))

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

x = 1.24904 \dots + πn

Solution steps

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

Subtract

\frac{1}{cos ( x )}

from both sides

\frac{3}{sin ( x )} - \frac{1}{cos ( x )} = 0

Simplify

\frac{3}{sin ( x )} - \frac{1}{cos ( x )} : \frac{3 cos ( x ) - sin ( x )}{sin ( x ) cos ( x )}

\frac{3 cos ( x ) - sin ( x )}{sin ( x ) cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

3 cos (x) - sin (x) = 0

Rewrite using trig identities

3 - tan (x) = 0

Move

3

to the right side

- tan (x) = - 3

Divide both sides by

- 1

tan (x) = 3

Apply trig inverse properties

x = arctan (3) + πn

Show solutions in decimal form

x = 1.24904 \dots + πn

2 cos (t) - 2 sin (2 t) = 0

4 sin (x) = - 2 cos (x)

3 sin (2 x) = 1.5

sin (2 x - 5 0^{\circ}) = - \frac{1}{2}

x, cos (x) = \frac{4}{5}

What is the general solution for 3/(sin(x))= 1/(cos(x)) ?
The general solution for 3/(sin(x))= 1/(cos(x)) is x=1.24904…+pin