What is the general solution for cos(pi+x)+cos(pi+x)=1 ?

The general solution for cos(pi+x)+cos(pi+x)=1 is x= pi/3+2pin-pi,x=(5pi)/3+2pin-pi

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cos(pi+x)+cos(pi+x)=1

cos (π + x) + cos (π + x) = 1

x = \frac{π}{3} + 2 πn - π, x = \frac{5 π}{3} + 2 πn - π

Degrees

x = - 12 0^{\circ} + 36 0^{\circ} n, x = 12 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (π + x) + cos (π + x) = 1

Simplify

cos (π + x) + cos (π + x) : 2 cos (π + x)

cos (π + x) + cos (π + x)

Add similar elements:

cos (x + π) + cos (x + π) = 2 cos (x + π)

= 2 cos (x + π)

2 cos (π + x) = 1

Divide both sides by

2

2 cos (π + x) = 1

Divide both sides by

2

\frac{2 cos ( π + x )}{2} = \frac{1}{2}

Simplify

cos (π + x) = \frac{1}{2}

cos (π + x) = \frac{1}{2}

General solutions for

cos (π + x) = \frac{1}{2}

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}

π + x = \frac{π}{3} + 2 πn, π + x = \frac{5 π}{3} + 2 πn

π + x = \frac{π}{3} + 2 πn, π + x = \frac{5 π}{3} + 2 πn

Solve

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

π + x = \frac{π}{3} + 2 πn

Move

π

to the right side

π + x = \frac{π}{3} + 2 πn

Subtract

π

from both sides

π + x - π = \frac{π}{3} + 2 πn - π

Simplify

x = \frac{π}{3} + 2 πn - π

x = \frac{π}{3} + 2 πn - π

Solve

π + x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{3} + 2 πn - π

π + x = \frac{5 π}{3} + 2 πn

Move

π

to the right side

π + x = \frac{5 π}{3} + 2 πn

Subtract

π

from both sides

π + x - π = \frac{5 π}{3} + 2 πn - π

Simplify

x = \frac{5 π}{3} + 2 πn - π

x = \frac{5 π}{3} + 2 πn - π

x = \frac{π}{3} + 2 πn - π, x = \frac{5 π}{3} + 2 πn - π

1 + 2 sin (θ) = 0

x, z = arcsin (x y)

2 cos (x) - 2 = 0

4 sin^{2} (θ) - 13 sin (θ) + 9 = 0

23 cos^{2} (x) = sin (x)

What is the general solution for cos(pi+x)+cos(pi+x)=1 ?
The general solution for cos(pi+x)+cos(pi+x)=1 is x= pi/3+2pin-pi,x=(5pi)/3+2pin-pi