Question

If 3x = cosec θ and 3/x = cot θ, find the value of 3(x2 – 1/x2).​

Answer 1

Answer:

as we know that cosec^2theta - cot^2 theta =1

then we will use this dentity

(3x) ^2-(3/x) ^2=1 (equation.1)

{because in question it is given that cosec theta =3x

and cot theta =3/x

now by equation 1

opening square

9x^2 - 9/x^2= 1

taking 9 common

9(x^2-1/x^2) =1

3.3 ( x^2 -1/X^2) =1

then taking 3 to right side

3(X^2-1/x^2) = 1/3

hence the ans is 1/3