Question

if cosecø +cot∅ = p then prove that cos∅ = p^2-1/p^2+1​

Answer 1

cosec θ + cot θ= P (given)

we know,

cosec² θ - cot² θ = 1

(cosec θ + cot θ)( cosec θ - cot θ)= 1

(cosec θ - cot θ) × P = 1

( cosec θ - cot θ) = 1/P

Let's solve (i ) and (ii)

cosec θ = 1+ P²/2P

cot θ = P²-1/2P

cot θ / cosec θ= (P²-1/2P)×(2P/P2²+1)

cos θ = P²-1/P²+1