Question

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

Answer 1

theta = 45
so 4+ cot 45 = 4+1 =5

you are given cot theta is equal to 1 .. cot (1) is known as 45°

Answer 2

given that costheta =1/root 2

we have the identities
  sin square theta + cos square theta=1
from this sin theta =1/root 2
then,
cosec theta =root 2
and again we have identity cosec square theta -cot square theta =1
then ,
cot theta =1
4+cot theta =4+1=5