What is the general solution for (sin(2x))/(cos(x))=0 ?

The general solution for (sin(2x))/(cos(x))=0 is x=pin

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(sin(2x))/(cos(x))=0

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

x = πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n

Solution steps

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

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

sin (2 x) = 0

General solutions for

sin (2 x) = 0

sin (x)

periodicity table with

2 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

2 x = 0 + 2 πn, 2 x = π + 2 πn

2 x = 0 + 2 πn, 2 x = π + 2 πn

Solve

2 x = 0 + 2 πn : x = πn

2 x = 0 + 2 πn

0 + 2 πn = 2 πn

2 x = 2 πn

Divide both sides by

2

2 x = 2 πn

Divide both sides by

2

\frac{2 x}{2} = \frac{2 πn}{2}

Simplify

x = πn

x = πn

Solve

2 x = π + 2 πn : x = \frac{π}{2} + πn

2 x = π + 2 πn

Divide both sides by

2

2 x = π + 2 πn

Divide both sides by

2

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

Simplify

x = \frac{π}{2} + πn

x = \frac{π}{2} + πn

x = πn, x = \frac{π}{2} + πn

Since the equation is undefined for:

\frac{π}{2} + πn

x = πn

12 sin^{2} (x) = 5 cos (x) + 9

cos (θ) = - \frac{2 5}{5}

cos (2 a) + cos (a) = 0

536 = 100 + 759 \cdot tan (x)

cos^{2} (x) = cos^{2} (x) csc (x)

What is the general solution for (sin(2x))/(cos(x))=0 ?
The general solution for (sin(2x))/(cos(x))=0 is x=pin