What is the general solution for (cos(x)+3cos(x))/(2+2)=0 ?

The general solution for (cos(x)+3cos(x))/(2+2)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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(cos(x)+3cos(x))/(2+2)=0

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

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

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Simplify

\frac{cos ( x ) + 3 cos ( x )}{2 + 2} : cos (x)

\frac{cos ( x ) + 3 cos ( x )}{2 + 2}

Add similar elements:

cos (x) + 3 cos (x) = 4 cos (x)

= \frac{4 cos ( x )}{2 + 2}

Add the numbers:

2 + 2 = 4

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

Divide the numbers:

\frac{4}{4} = 1

= cos (x)

cos (x) = 0

General solutions for

cos (x) = 0

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

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

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

3 tan^{3} (x) - tan^{2} (x) - tan (x) - 1 = 0

cos (2 x + 60) = cos (x)

3 tan (x) - 3 cot (x) - 1 = 0

5 sin^{2} (x) + 6 cos (x) - 6 = 0

sin^{2} (x) - sin (x) cos (x) - 6 cos^{2} (x) = 0

What is the general solution for (cos(x)+3cos(x))/(2+2)=0 ?
The general solution for (cos(x)+3cos(x))/(2+2)=0 is x= pi/2+2pin,x=(3pi)/2+2pin