Question

If 3x=cosec theta and 3/x=cot theta then find 3(x^2-1/x^2)

Answer 1

Answer for this is 1/3

Answer 2

Answer:

$\frac{1}{3}$

Step-by-step explanation:

As per the question,

We have been provided that,

cosecθ = 3x

cotθ = 3/x

To find :

$3(x^{2}-\frac{1}{x^{2}})$

Solution:

On simplifying the equation and multiplying by the number '3' in the both 'Numerator' and 'Denominator' we get,

$3(x^{2}-\frac{1}{x^{2}})=3(x+\frac{1}{x})(x-\frac{1}{x})=\frac{3(x+\frac{1}{x})(x-\frac{1}{x})\times 3}{3}\\=\frac{(3x+\frac{3}{x})(3x-\frac{3}{x})}{3}$

Therefore, now,

On putting the values from the given values of 'cosecθ' and 'cotθ', we get,

$\frac{(3x+\frac{3}{x})(3x-\frac{3}{x})}{3}=\frac{(cosec\theta+cot\theta)(cosec\theta-cot\theta)}{3}=\frac{cosec^{2}\theta-cot^{2}\theta}{3}\\\frac{cosec^{2}\theta-cot^{2}\theta}{3}=\frac{1}{3}$

Hence, the value of the given equation is given by,

$\frac{1}{3}$