Question

Prove the following trigonometric identities. If cosec θ + cot θ = m and cosec θ − cot θ = n, prove that mn = 1

Answer 1

Answer with Step-by-step explanation:

Given :  

cosec θ + cot θ = m …………(1)

cosec θ − cot θ = n……….(2)

On multiplying eq 1 & 2,

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

(cosec²θ -  cot²θ) = mn

[By using identity , (a + b) (a - b) = a² - b²]

 (1/sin²θ - cos²θ/sin²θ) = mn

[By using, cosecθ = 1/sinθ]

(1 - cos²θ)/sin²θ = mn

[By taking LCM]

sin²θ / sin²θ = mn

[By using  an identity, (1- cos²θ) = sin²θ]

1 = mn

mn = 1

Hence Proved..

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer:

Step-by-step explanation:

L.H.S:

(cosec θ + cot θ)(cosec θ − cot θ)

=> cosec²θ - cot²θ

//remember the identity cosec²θ - cot²θ = 1

=> 1

=> R.H.S