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

The general solution for cot(x)=(sin(x))/(cos(x)) is x= pi/4+pin,x=(3pi)/4+pin

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cot(x)=(sin(x))/(cos(x))

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

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Solution steps

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

Subtract

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

from both sides

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

Simplify

cot (x) - \frac{sin ( x )}{cos ( x )} : \frac{cot ( x ) cos ( x ) - sin ( x )}{cos ( x )}

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

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

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

Express with sin, cos

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

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

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

Rewrite using trig identities

cos (2 x) = 0

General solutions for

cos (2 x) = 0

2 x = \frac{π}{2} + 2 πn, 2 x = \frac{3 π}{2} + 2 πn

Solve

2 x = \frac{π}{2} + 2 πn : x = \frac{π}{4} + πn

Solve

2 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{4} + πn

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

0.6 = \frac{cosh ( 0.2 m )}{cosh ( 0.4 m )}

12 cos (2 x) + 5 sin (x) - 9 = 0

sin (x) = \frac{4}{8}

csc (a) = - 1

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

What is the general solution for cot(x)=(sin(x))/(cos(x)) ?
The general solution for cot(x)=(sin(x))/(cos(x)) is x= pi/4+pin,x=(3pi)/4+pin