Given, cot θ=34
We know that, cot θ=adjacent sideopposite side=34 [given]
Now,
⇒Hypotenuse2=adjacent side2+opposite side2⇒Hypotenuse2=32+42⇒Hypotenuse2=25⇒Hypotenuse=5
sec θ=hypotenuseadjacent side=53cosec θ=hypotenuseopposite side=54
Now, we will put values i.e.
=√(sec θ − cosec θsec θ + cosec θ)=√(53−5453+54)=5123512=535=1√7
Hence, proved.