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

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

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

solve for

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

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

Solution steps

cos (x + y) = - cos (x)

Subtract

- cos (x)

from both sides

cos (x + y) + cos (x) = 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}

4 + 2 tan^{2} (x) = 5 tan^{2} (x) + 3

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

θ, sec (θ) = 2

2 cos (4 θ) = 0

\frac{1032}{3145} sin (4 x) + \frac{2196}{3145} cos (4 x) = 0

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