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If f(x)=cos2x+4sinx+5, then the differen...

If `f(x)=cos2x+4sinx+5,` then the difference of maximum and minimum values of `f(x)` is

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Let f(x)=[(sin^2x,sinx,1),(sinx,1,sin^2x),(1,sin^2x,sinx)] and g(x)=[(cos^2x,cosx,1),(cosx,1,cos^2x),(1,cos^2x,cosx)]. If h(x)=Tr.(f(x)g(x)), then find the absolute value of the difference between maximum and minimum value of h(x). [Tr. (P) denotes the trace of Matrix P]