If cotθ =√3, find the value of cosec^2θ + cot^2θ/cosec^2θ - sec^2θ

Question

If cotθ =√3, find the value of \(\frac{cosec^2θ + cot^2θ}{cosec^2θ - sec^2θ}\)

Answer 1

Given, cotθ = √3 

cosec²θ = 1 + cot²θ = 1 + (√3)² 

= 1 + 3 = 4 

and cotθ =√3 ⇒ tanθ = \(\frac{1}{\sqrt{3}}\) 

⇒ sec²θ = 1 + tan²θ = 1 + \(\Big(\frac{1}{\sqrt{3}}\Big)^2\) = 1 + \(\frac{1}{{3}}\) = \(\frac{4}{3}\)

Now,