What is the general solution for cos(x)-5=-4-sin(x) ?

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

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cos(x)-5=-4-sin(x)

cos (x) - 5 = - 4 - sin (x)

x = 2 πn, x = 2 πn + \frac{π}{2}

Solution steps

cos (x) - 5 = - 4 - sin (x)

Subtract

- 4 - sin (x)

from both sides

cos (x) + sin (x) - 1 = 0

Rewrite using trig identities

- 1 + 2 sin (x + \frac{π}{4}) = 0

Move

1

to the right side

2 sin (x + \frac{π}{4}) = 1

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (x + \frac{π}{4}) = \frac{2}{2}

x + \frac{π}{4} = \frac{π}{4} + 2 πn, x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

Solve

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

Solve

x + \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = 2 πn + \frac{π}{2}

x = 2 πn, x = 2 πn + \frac{π}{2}

sin (d) = 0.19

2 sin^{2} (4 x) = 1

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

x, y = sin (x) y

1 \cdot sin (x) = 1.5 \cdot sin (\frac{x}{2})

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