​ If cosec θ + cot θ = p, show that p^2 +1 / p^2 -1 = sec θ. ​

Question

If cosec θ + cot θ = p, show that \(\frac{p^2+1}{p^2-1}\) = sec θ.

p2 +1 / p² -1 = sec θ.  ​

Answer 1

cosec θ – cot θ = p 

∴ cosec θ – cot θ = \(\frac{1}{p}\) ……………….(1) 

cosec θ + cot θ = p …………..(2) 

(1) + (2), We get 

2 cosec θ = p + \(\frac{1}{p}\) = \(\frac{p^2+1}{p^2-1}\) …………..(3) 

cosec θ – cot θ = p 

cosec θ – cot θ = \(\frac{1}{p}\)

(1) – (2), We get

Hence proved.