Question

Solve the equation on the
interval [0,21).
2 csc x + 17 = 15 + CSC X

Answer 1

Answer:

7π/6, 11π/6

Step-by-step explanation:

2cscx + 17 = 15 + cscx

1. Subtract cscx and 17 from both sides ⇒ cscx = -2

2. cscx = 1/sinx ⇒ 1/sinx = -2

3. Multiply by sinx and divide by -2 ⇒ sinx = -1/2

When is sinx equal to -1/2? ⇒ 7π/6, 11π/6

Answer 2

The solution of the equation 2cosec x+17 = 15+cosec x is 7π/6 and 11π/6.

What is the solution of the given equation in the interval [0, 2π)?

Given:

• The equation which is given is 2Cosec x + 17 = 15 + Cosec x.
• The interval is [0,2π).

Find:

• The solution of the given equation.

Solution:

2Cosec x + 17 = 15 + Cosec x

⇒ 2Cosec x - Cosec x = 15 - 17

⇒ Cosec x = -2

Now, 1/sinx = -2

   ⇒  sinx = -1/2

we know, sin 30° = 1/2

Since, sinx is negative,

x will be in 3rd and 4th quadrant.

value in 3rd quadrant = 180° + 30° = 210°

value in 4th quadrant = 360° - 30° = 330°

So, x = 210° = 210 * π/180 = 7π/6

Also, x = 330° = 330 * π/180 = 11π/6

To learn more about the equation on the interval, refer to:

https://brainly.com/question/14266131

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