The correct option is (b) \[\mathbf{1}\]
Given, \[\mathbf{3}\text{ }\mathbf{ta}{{\mathbf{n}}^{-\mathbf{1}}}~\mathbf{x}\text{ }+\text{ }\mathbf{co}{{\mathbf{t}}^{-\mathbf{1}}}~\mathbf{x}\text{ }=\text{ }\mathbf{\pi }\]
\[\begin{array}{*{35}{l}}
2\text{ }ta{{n}^{-1}}~x\text{ }+\text{ }ta{{n}^{-1}}~x\text{ }+\text{ }co{{t}^{-1}}~x\text{ }=\text{ }\pi \\
2\text{ }ta{{n}^{-1}}~x\text{ }+\text{ }\pi /2\text{ }=\text{ }\pi \text{ }(As\text{ }ta{{n}^{-1}}~+\text{ }co{{t}^{-1}}~=\text{ }\pi /2) \\
2\text{ }ta{{n}^{-1}}~x\text{ }=\text{ }\pi /2 \\
ta{{n}^{-1}}~x\text{ }=\text{ }\pi /4 \\
x\text{ }=\text{ }1 \\
\end{array}\]