What is the general solution for solvefor x,cos(xy)-sin(xy)=2 ?

The general solution for solvefor x,cos(xy)-sin(xy)=2 is No Solution for x\in\mathbb{R}

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solvefor x,cos(xy)-sin(xy)=2

solve for

x, cos (x y) - sin (x y) = 2

No Solution for x \in R

Solution steps

cos (x y) - sin (x y) = 2

Subtract

2

from both sides

cos (x y) - sin (x y) - 2 = 0

Rewrite using trig identities

- 2 - 2 sin (\frac{4 x y - π}{4}) = 0

Move

2

to the right side

- 2 sin (\frac{4 x y - π}{4}) = 2

Divide both sides by

- 2

sin (\frac{4 x y - π}{4}) = - 2

- 1 \leq sin (x) \leq 1

No Solution for x \in R

2 sin^{2} (x) - sin (x) - 2 = 0

4 cos^{2} (x) - 6 = 5 cos (x)

tan (θ) = \frac{- 3}{2}

7 sin (x + 5) = 1

2 sin (x) tan (2 x) - 3 tan (2 x) = 0

What is the general solution for solvefor x,cos(xy)-sin(xy)=2 ?
The general solution for solvefor x,cos(xy)-sin(xy)=2 is No Solution for x\in\mathbb{R}