Question

If 3x=cosec theeta and 3/x = cot theeta, find the value of 3 (x^2-1/x^2)​

Answer 1

Answer

1/3

Solution

Given

3x = cosec∅

3/x = cot∅

To find

The value of 3(x² - 1/x²)

3x = cosec∅

Squaring both sides, we get

9x² = cosec²∅ .......(1)

3/x = cot∅

Squaring both sides, we get

9/x² = cot²∅ ..........(2)

Subtract (2) from (1)

9x² - 9/x² = cosec²∅ - cot²∅

We know that cosec²∅ - cot²∅ = 1

→ 9(x² - 1/x²) = 1

Divine both sides by 3,

3(x² - 1/x²) = 1/3

Answer 2

$\huge\bold\green{AnsWer }$

$\bold\green{GiVen }$

→3x = cosec∅

→3/x = cot∅

$\bold\green{To \: Find }$

Acc. to the question we have to find value of 3(x² - 1/x²)

3x = cosec∅

Squaring both sides, we get

9x² = cosec²∅ ________________________(¡)

3/x = cot∅

Squaring both sides, we get

9/x² = cot²∅ _________________________(¡¡)

By Subtracting eqn. (2) from (1)

9x² - 9/x² = cosec²∅ - cot²∅

Formula :- [cosec²∅ - cot²∅ = 1]

→ 9(x² - 1/x²) = 1

By dividing both sides by 3

3(x² - 1/x²) = 1/3