What is the general solution for (cos(x))/(tan(x))= 3/2 ?

The general solution for (cos(x))/(tan(x))= 3/2 is x= pi/6+2pin,x=(5pi)/6+2pin

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(cos(x))/(tan(x))= 3/2

\frac{cos ( x )}{tan ( x )} = \frac{3}{2}

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

\frac{cos ( x )}{tan ( x )} = \frac{3}{2}

Subtract

\frac{3}{2}

from both sides

\frac{cos ( x )}{tan ( x )} - \frac{3}{2} = 0

Simplify

\frac{cos ( x )}{tan ( x )} - \frac{3}{2} : \frac{2 cos ( x ) - 3 tan ( x )}{2 tan ( x )}

\frac{2 cos ( x ) - 3 tan ( x )}{2 tan ( x )} = 0

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

2 cos (x) - 3 tan (x) = 0

Express with sin, cos

\frac{2 cos ^{2} ( x ) - 3 sin ( x )}{cos ( x )} = 0

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

2 cos^{2} (x) - 3 sin (x) = 0

Rewrite using trig identities

(1 - sin^{2} (x)) \cdot 2 - 3 sin (x) = 0

Solve by substitution

sin (x) = - 2, sin (x) = \frac{1}{2}

sin (x) = - 2 :

No Solution

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

cos (2 x) + 5 cos (x) = 3

sin (θ) = \frac{207.91 \cdot sin ( 31.7697 7 ^{\circ} )}{238.99}

15 = - 40 sin (18 (x - 10))

tan^{2} (x) - tan (x) - 6 = 0

\frac{1}{sec ( 2 x ) - 1} - \frac{1}{sec ( 2 x ) + 1} = 6

What is the general solution for (cos(x))/(tan(x))= 3/2 ?
The general solution for (cos(x))/(tan(x))= 3/2 is x= pi/6+2pin,x=(5pi)/6+2pin