Question

please give me answer i will mark as brilient

Answer 1

cos(90-theta) = sin theta

sin theta + cos theta = root2*sin theta
1 + cot theta = root2 [both l.h.s and r.h.s divided by sin theta]
cot theta = root2 - 1
Option B
Hope it helps.

Answer 2

Hi, friend

$sinx +cosx = \sqrt{2} \cos(90 - x )$
you do know
here
$cosx(90 - x) = sinx$
then
$\sin(x) + \cos(x) = \sqrt{2} \sin(x)$
after deviding by sinx
$1 + \cot(x) = \sqrt{2}$
$\cot(x) = \sqrt{2 } - 1$
I hope you understand