Solve the following equation on the interval [0°,360°)[0°,360°). Round answers to the nearest tenth. If there is no solution, indicate "No Solution."9csc2(x)−15cot(x)=39csc2(𝑥)−15cot(𝑥)=3AnswerHow to enter your answer (opens in new window)2 PointsKeypadKeyboard ShortcutsChoose the correct answer from the options below. 225°225° 236.3°236.3° 45°,225°,56.3°,236.3°45°,225°,56.3°,236.3° 45°,225°,56.3°,596.3°

The question seems to be a bit jumbled, but it appears to be asking to solve the trigonometric equation 9csc^2(x) - 15cot(x) = 3 on the interval [0°,360°).

First, let's rewrite the equation in terms of sine and cosine:

9/sin^2(x) - 15cos(x)/sin(x) = 3

Multiply through by sin^2(x) to clear the fractions:

9 - 15cos(x) = 3sin^2(x)

Rearrange the equation to get a quadratic in terms of cos(x):

3sin^2(x) + 15cos(x) - 9 = 0

Substitute y = cos(x):

3(1-y^2) + 15y - 9 = 0

Expand and simplify:

3 - 3y^2 + 15y - 9 = 0

-3y^2 + 15y - 6 = 0

Divide through by -3:

y^2 - 5y + 2 = 0

Factor the quadratic:

(y - 2)(y - 1) = 0

Set each factor equal to zero and solve for y:

y - 2 = 0 => y = 2

y - 1 = 0 => y = 1

Substitute y = cos(x) back into the equation:

cos(x) = 2 => x = cos^-1(2) => No Solution (cosine values are between -1 and 1)

cos(x) = 1 => x = cos^-1(1) => x = 0°, 360°

So, the solution to the equation on the interval [0°,360°) is x = 0°, 360°. However, since the interval is not inclusive of 360°, the only solution is x = 0°.

Therefore, none of the provided options are correct. The correct answer should be 0°.