Question

if cosec theta+ cot theta = x,, find the value of cosec theta-cot theta ​

Answer 1

Solution :

By trigonometric identity, we know that

cosec²θ - cot²θ = 1

→ (cosecθ + cotθ) (cosecθ - cotθ) = 1

→ x * (cosecθ - cotθ) = 1

∴ cosecθ - cotθ = 1/x

Answer 2

Answer:

1/x

Step-by-step explanation:

cosec θ + cot θ = x

We know that :

cosec²θ - cot²θ = 1

Let us factorize the given expression :

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

We are given that cosec θ + cot θ = x

Hence :

x ( cosec θ - cot θ ) = 1

= > cosec θ - cot θ = 1/x

Thus the required value is 1/x .