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

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

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(cos(x))/(sin(x))=tan(x)

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

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

Solution steps

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

Subtract

tan (x)

from both sides

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

Simplify

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

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

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

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

Express with sin, cos

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

sin (B) = \frac{7 sin ( 3 6 ^{\circ} )}{12}

x, cos^{2} (x) = sin (y + \frac{π}{2})

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

sec^{2} (x) - tan^{2} (x) = cos (x)

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

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