A function f:R−{(2k−1)π}→R is defined as, f(x)=1√m2−n2ln(√m+n+√m−ntan(x/2)√m+n−√m−ntan(x/2)) where k,m,n∈Z+ and n<mIf f′(π3)=19, then which of the following ordered pairs of (m,n) is/are correct?

A function f:R−{(2k−1)π}→R is defined as, f(x)=1√m2−n2ln(�

1.	A function f:R−{(2k−1)π}→R is defined as, f(x)=1√m2−n2ln(√m+n+√m−ntan(x/2)√m+n−√m−ntan(x/2)) where k,m,n∈Z+ and n<mIf f′(π3)=19, then which of the following ordered pairs of (m,n) is/are correct?
Answer» A function $f : R - {(2 k - 1) π} \to R$ is defined as, $f (x) = \frac{1}{\sqrt{m^{2} - n^{2}}} ln (\frac{\sqrt{m + n} + \sqrt{m - n} tan (x / 2)}{\sqrt{m + n} - \sqrt{m - n} tan (x / 2)})$ where $k, m, n \in Z^{+}$ and $n < m$ If $f^{'} (\frac{π}{3}) = \frac{1}{9}$ , then which of the following ordered pairs of $(m, n)$ is/are correct?