What is the general solution for (sin(x)+2)(tan(x)-2)=0 ?

The general solution for (sin(x)+2)(tan(x)-2)=0 is x=1.10714…+pin

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

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

x = 1.10714 \dots + πn

Degrees

x = 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Solving each part separately

sin (x) + 2 = 0 or tan (x) - 2 = 0

sin (x) + 2 = 0 :

No Solution

sin (x) + 2 = 0

Move

2

to the right side

sin (x) + 2 = 0

Subtract

2

from both sides

sin (x) + 2 - 2 = 0 - 2

Simplify

sin (x) = - 2

sin (x) = - 2

- 1 \leq sin (x) \leq 1

No Solution

tan (x) - 2 = 0 : x = arctan (2) + πn

tan (x) - 2 = 0

Move

2

to the right side

tan (x) - 2 = 0

Add

2

to both sides

tan (x) - 2 + 2 = 0 + 2

Simplify

tan (x) = 2

tan (x) = 2

Apply trig inverse properties

tan (x) = 2

General solutions for

tan (x) = 2

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (2) + πn

x = arctan (2) + πn

Combine all the solutions

x = arctan (2) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn

sec^{2} (x) + 4 sec (x) - 12 = 0

sin (θ) = - 1, 0^{\circ} \leq θ < 36 0^{\circ}

3 cos^{2} (x) + sin (x) + 1 = 0

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

sin (x) = 7

What is the general solution for (sin(x)+2)(tan(x)-2)=0 ?
The general solution for (sin(x)+2)(tan(x)-2)=0 is x=1.10714…+pin