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For \( 0x\frac{\pi}{2} \), let \( P_{\mathrm{mn}}(x)=m \log _{\cos x}(\sin x)+n \log _{\cos x}(\cot x) \); where \( m, n \in\{1,2, \ldots, 9\} \)
P
[For example :
W
\[
\begin{array}{l}
P_{29}(x)=2 \log _{\cos x}(\sin x)+9 \log _{\cos x}(\cot x) \text { and } \\
\left.P_{77}(x)=7 \log _{\cos x}(\sin x)+7 \log _{\cos x}(\cot x)\right]
\end{array}
\]
On the basis of above information , answer the following questions :
If \( P_{34}(x)=P_{22}(x) \), then the value of \( \sin x \) is expressed as \( \left(\frac{\sqrt{q}-1}{p}\right) \), then \( (p+q) \) equals
(a) 3
(b) 4
(c) 7
(d) 9
Note Mean proportional of \( a \) and \( b(a0, b0) \) is \( \sqrt{a b} \) ]
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