Question

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

Answer 1

(3x)^2 = cosec^2 theta
So , 9x^2 = cosec^2 theta

Also , (3/x) ^2 = cot^2 theta

9/(x^2) = cot^2 theta

we know that , cosec^2 θ -cot^2θ = 1

so ,  9x^2 - 9/(x^2) = 1

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

we have to find , 3(x^2 - 1/x^2)

So , it is equal to , 3(1/9) = 1/3

Hope this helps !
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