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

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

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solvefor x,cos(x-y)=0

solve for

x, cos (x - y) = 0

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

Solution steps

cos (x - y) = 0

General solutions for

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

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

Solve

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

x - y = \frac{π}{2} + 2 πn

Move

y

to the right side

x - y = \frac{π}{2} + 2 πn

Add

y

to both sides

x - y + y = \frac{π}{2} + 2 πn + y

Simplify

x = \frac{π}{2} + 2 πn + y

x = \frac{π}{2} + 2 πn + y

Solve

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

x - y = \frac{3 π}{2} + 2 πn

Move

y

to the right side

x - y = \frac{3 π}{2} + 2 πn

Add

y

to both sides

x - y + y = \frac{3 π}{2} + 2 πn + y

Simplify

x = \frac{3 π}{2} + 2 πn + y

x = \frac{3 π}{2} + 2 πn + y

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

sin (a) + 1 = 2 1 - sin^{2} (a)

4 cos (x) - 3 = 0

cos (θ) cos (2 θ) + sin (θ) sin (2 θ) = \frac{1}{2}

8 sin (x) tan (x) + tan (x) = 0

sin (x) - 3 = cos (x) - 3

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