Question

if cos theta is equals to 1 by root 2 then find the value of 4 + cot theta​

Answer 1

I hope this is what you're trying to ask,

$\cos(a) = \frac{1}{ \sqrt{2} }$
[I have used alpha insead of theta since I can't find the sign on my keyboard]

then,
$4 + \cos( \alpha ) \\ = 4 + \frac{1}{ \sqrt{2} } \\ = \frac{4 \sqrt{2} + 1 }{ \sqrt{2} } \\ = \frac{8 + \sqrt{2} }{2}$