What is the general solution for cos(x)+2sin(x)+3=0 ?

The general solution for cos(x)+2sin(x)+3=0 is No Solution for x\in\mathbb{R}

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cos(x)+2sin(x)+3=0

cos (x) + 2 sin (x) + 3 = 0

No Solution for x \in R

Solution steps

cos (x) + 2 sin (x) + 3 = 0

Subtract

2 sin (x)

from both sides

cos (x) + 3 = - 2 sin (x)

Square both sides

(cos (x) + 3)^{2} = (- 2 sin (x))^{2}

Subtract

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

from both sides

(cos (x) + 3)^{2} - 4 sin^{2} (x) = 0

Rewrite using trig identities

5 + 5 cos^{2} (x) + 6 cos (x) = 0

Solve by substitution

cos (x) = - \frac{3}{5} + i \frac{4}{5}, cos (x) = - \frac{3}{5} - i \frac{4}{5}

cos (x) = - \frac{3}{5} + i \frac{4}{5} :

No Solution

cos (x) = - \frac{3}{5} - i \frac{4}{5} :

No Solution

Combine all the solutions

No Solution

Verify solutions by plugging them into the original equation

No Solution for x \in R

x, arccos (x) = 1

cos (x) + 2 sin (x) = - 1

csc (x) = - 7

cos (4 t) + sin (4 t) = 0

cos (x - 3 0^{\circ}) = 0.22

What is the general solution for cos(x)+2sin(x)+3=0 ?
The general solution for cos(x)+2sin(x)+3=0 is No Solution for x\in\mathbb{R}