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A=[1t a n x-t a n x1]a n df(x) is define...

`A=[1t a n x-t a n x1]a n df(x)` is defined as `f(x)=d e tdot(A^T A^(-1))` en the value of `(f(f(f(ff(x))))_` is `(ngeq2)` _________.

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The correct Answer is:
2
`because A = [[1,tan x],[-tan x,1]]`
`therefore det A + [[1, tan x],[-tan x, 1]]= (1+ tan^(2)x) = ""^(2)x`
`rArr det A^(T) = det A = sec^(2) x `
Now, `f(x) = det (A^(T) A^(-1)) = (det A^(T)) (detA^(-1))`
`= ( det A^(T) ) (det A)^(-1) = (det(A^(T)))/(detA)= 1 `
`therefore underset("n times")(underbrace(lambda = f(f(f(f...f(x))))))=1 [because f(x) = 1]`
Hence, `2^(lambda)= 2^(1) = 2`
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