If A= dia. (d1,d2,d3,d4) where di>0 ∀ i=1,2,3,4 is a diagonal matrix – InterviewSolution

1.	If A= dia. (d1,d2,d3,d4) where di>0 ∀ i=1,2,3,4 is a diagonal matrix of order 4 such that d1+2d2+4d3+8d4=16, then the maximum value of f(x)=log(tanx+cotx)(det(A)) where x∈(0,π2) is equal to
Answer» If $A =$ dia. $(d_{1}, d_{2}, d_{3}, d_{4})$ where $d_{i} > 0 \forall i = 1, 2, 3, 4$ is a diagonal matrix of order $4$ such that $d_{1} + 2 d_{2} + 4 d_{3} + 8 d_{4} = 16,$ then the maximum value of $f (x) = {log}_{(tan x + cot x)} (det (A))$ where $x \in (0, \frac{π}{2})$ is equal to

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