Solve exactly for $x$ for $720^{\circ} \leq x \leq 900^{\circ}$ .
$\cos^{3} x + \cos x \sin^{2} x = \sin x$

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Final Answer: The solution to the equation $\cos^{3} x + \cos x \sin^{2} x = \sin x$ for $4 π \leq x \leq 5 π$ is $x = \frac{17 π}{4}$ .

Steps

Step 1 ：The given equation is in terms of trigonometric functions. We can simplify the equation by using the Pythagorean identity $\sin^{2} x + \cos^{2} x = 1$ .

Step 2 ：We can also convert the given range of $x$ from degrees to radians because trigonometric functions use radians. The range $720^{\circ} \leq x \leq 900^{\circ}$ is equivalent to $4 π \leq x \leq 5 π$ in radians.

Step 3 ：Let's solve the equation $\sin (x)^{2} \cos (x) - \sin (x) + \cos (x)^{3} = 0$ for $x$ .

Step 4 ：The solution to the equation is $x = \frac{17 π}{4}$ .

Step 5 ：Final Answer: The solution to the equation $\cos^{3} x + \cos x \sin^{2} x = \sin x$ for $4 π \leq x \leq 5 π$ is $x = \frac{17 π}{4}$ .

Solve exactly for x for 720∘≤x≤900∘.cos3⁡x+cos⁡xsin2⁡x=sin⁡x

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Solve exactly for $x$ for $720^{\circ} \leq x \leq 900^{\circ}$ .
$\cos^{3} x + \cos x \sin^{2} x = \sin x$