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

The general solution for solvefor x,cos(x)-sin(x+y)=0 is x=2pin-y/2+pi/4 ,x=-y/2+(5pi)/4+2pin

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

solve for

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

x = 2 πn - \frac{y}{2} + \frac{π}{4}, x = - \frac{y}{2} + \frac{5 π}{4} + 2 πn

Solution steps

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

Rewrite using trig identities

- 2 sin (\frac{π - 2 y}{4}) sin (\frac{4 x - π + 2 y}{4}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

sin (\frac{4 x - π + 2 y}{4}) = 0

General solutions for

sin (\frac{4 x - π + 2 y}{4}) = 0

\frac{4 x - π + 2 y}{4} = 0 + 2 πn, \frac{4 x - π + 2 y}{4} = π + 2 πn

Solve

\frac{4 x - π + 2 y}{4} = 0 + 2 πn : x = 2 πn - \frac{y}{2} + \frac{π}{4}

Solve

\frac{4 x - π + 2 y}{4} = π + 2 πn : x = - \frac{y}{2} + \frac{5 π}{4} + 2 πn

x = 2 πn - \frac{y}{2} + \frac{π}{4}, x = - \frac{y}{2} + \frac{5 π}{4} + 2 πn

sin (x) = - cos (4 x)

cos (θ) = \frac{2}{3 38}

sec (x) cos (x) = sin (x)

tan (θ) - 1 - 2 = sec (θ)

3 cos (2 x) + 4 cos (4 x) - 5 = 0

What is the general solution for solvefor x,cos(x)-sin(x+y)=0 ?
The general solution for solvefor x,cos(x)-sin(x+y)=0 is x=2pin-y/2+pi/4 ,x=-y/2+(5pi)/4+2pin