Question

Question 3.
If cosec θ + cot θ = x, find the value of cosec θ – cot θ​

Answer 1

Answer:

cosec θ – cot θ= 1/x

Step-by-step explanation:

if cosec θ + cot θ = x

we know the identity

(cosec θ) ^2 - (cot θ) ^2 = 1

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

x (cosec θ – cot θ) = 1

cosec θ – cot θ= 1/x

Answer 2

Answer:

$\frac{1}{x}$

Step-by-step explanation:

cosec θ + cot θ = x ---------( 1 )

We know that,

cosec²θ = 1 + cot²θ ( Trignometric identity)

i.e. cosec²θ-cot²θ = 1

By using Identity, a²-b²= (a+b)(a-b)

(cosec θ +cot θ)(cosec θ- cot θ) = 1

( x )(cosec θ- cot θ) = 1

cosecθ - cotθ = 1/x

Final answer-

$(cosec θ- cot θ) = \frac{1}{x}$