Solution:
Given:
$\tan5\text{x}=\cot2\text{x}$
$\Rightarrow\tan5\text{x}=\tan\Big(\frac{\pi}{2}-2\text{x}\Big)$
$\Rightarrow5\text{x}=\text{n}\pi+\frac{\pi}{2}-2\text{x}$
$\Rightarrow7\text{x}=\text{n}\pi+\frac{\pi}{2}$
$\Rightarrow\text{x}=\frac{\text{n}\pi}{7}+\frac{\pi}{14},\ \text{n}\in\text{Z}$
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If $\text{f(x)}=\cos^2\text{x}+\sec^2\text{x},$ then:
$\text{f(x)}<1$
$\text{f(x)}=1$
$2<\text{f(x)}<1$
$\text{f(x)}\geq2$
[Hint: $\text{A.M}\geq\text{G.M.}$]
In a $\triangle\text{ABC}$ if A is the point (1, 2) and equations of the median through B and C are respectively x + y = 5 and x = 4, then B is: