\(\begin{aligned} P & =\frac{\cos \left(\frac{\pi}{2}-2 x\right)+\sin x}{\sin x+\sin 2 x+\sin 3 x}=\frac{\sin 2 x+\sin x}{\sin 3 x+\sin x+\sin 2 x} \\ & =\frac{2 \sin x \cos x+\sin x}{2 \sin 2 x \cos x+\sin 2 x}=\frac{\sin x(2 \cos x+1)}{\sin 2 \times(2 \cos x+1)} \\ & =\frac{\sin x}{2 \sin x \cos x}=\frac{1}{2 \cos x}\end{aligned}\)