If 3x = cosecθ and 3/x cot θ then (x^2 - 1/x^2) = ?

Question

If 3x = cosecθ and  3/x = cot θ then\((x^2-\frac{1}{x^2})\)

(a) 1/27 

(b) 1/81 

(c) 1/3 

(d) 1/9

Answer 1

Correct answer is (c) 1/3

Given: 3x = cosec θ and 3/x = cot θ 

Also, We can deduce that x = cosecθ/3 and 1/x = cotθ/3 

So, substituting the values of x and 1 /x in the given expression, we get:

= 3/9 (cosec²θ − cot² θ)

= 1/3 [By using the identity:(cosec²θ − cot² θ = 1)]