Question

if cosec a= 3x and cot a= 3/x, then find the value of (x^2-1/x^2)

Answer 1

x = coseca/3
1/x = cota/3

(x²-1/x²) = (x+1/x)(x-1/x)

= (coseca/3 + cota/3)(coseca/3 - cota/3)
= 1/9 (coseca+ cota)(coseca - cota)
= 1/9 (cosec²a - cot²a)
= 1/9 (cot²a +1 - cot²a)
= 1/9 (1)
= 1/9
I hope you understand the approach.
All the best!

Answer 2

Answer:

$\frac{1}{9}$

Step-by-step explanation:

x =  $\frac{cosec}{3}$

$\frac{1}{x}$ =  $\frac{cot}{3}$

$\frac{x^{2}-1 }{x^{2} }$ = (x+1/x)(x-1/x)

= (coseca/3 + cota/3)(coseca/3 - cota/3)

= 1/9 (coseca+ cota)(coseca - cota)

= 1/9 (cosec²a - cot²a)

= 1/9 (1 )        [ since cosec²a - cot²a = 1 ]

= 1/9 (1)

= 1/9