A function $f$ is continuous for all $x$ (and not everywhere zero) such that $f^2\left(x\right)={\int }_0^{x}f\left(t\right)\frac{\cos t}{2+\sin t}dt\dot{}$ Then $f\left(x\right)$ is $\frac{1}{2}1n\left(\frac{x+\cos x}{2}\right);x\ne 0$$\frac{1}{2}1n\left(\frac{3}{x+\cos x}\right);x\ne 0$$\frac{1}{2}1n\left(\frac{2+\sin x}{2}\right);x\ne n\pi ,n\in I$$\frac{\cos x+\sin x}{2+\sin x};x\ne n\pi +\frac{3\pi }{4},n\in I$

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