Matrices 1

Calculus Level 2

Let 0<a<b<π20<a<b<\frac { \pi }{ 2 } . If f(x)=sinxsinasinbcosxcosacosbtanxtanatanbf\left( x \right) =\left| \begin{matrix} \sin { x } & \sin { a } & \sin { b } \\ \cos { x } & \cos { a } & \cos { b } \\ \tan { x } & \tan { a } & \tan { b } \end{matrix} \right| , then minimum possible number of roots of f(x)=0f'\left( x \right) =0 lying in (a,b)(a,b) is:

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