What is the general solution for solvefor x,cos(x)+cos(x+y)=0 ?

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

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solvefor x,cos(x)+cos(x+y)=0

solve for

x, cos (x) + cos (x + y) = 0

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

Solution steps

cos (x) + cos (x + y) = 0

Rewrite using trig identities

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

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

General solutions for

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

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

Solve

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

Solve

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

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

cosh (x) = 1

- 2 sin (x) - 1 = 0

3 sin (θ) + cos (θ) = 1

3 csc (x) + 2 = 0

2 cos^{2} (x) = sin (x) - 1

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