Final answer to the problem
$x=\frac{\arcsin\left(-2\right)}{2}$
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Step-by-step Solution
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1
Find the roots of the equation using the Quadratic Formula
$\frac{\cos\left(x\right)^3-\sin\left(x\right)^3}{\cos\left(x\right)-\sin\left(x\right)}=0$
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$\frac{\cos\left(x\right)^3-\sin\left(x\right)^3}{\cos\left(x\right)-\sin\left(x\right)}=0$
Learn how to solve problems step by step online. Find the roots of (cos(x)^3-sin(x)^3)/(cos(x)-sin(x)). Find the roots of the equation using the Quadratic Formula. Multiply both sides of the equation by \cos\left(x\right)-\sin\left(x\right). Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1.
Final answer to the problem
$x=\frac{\arcsin\left(-2\right)}{2}$