Question

If cosec θ = 2x and $$5(x^2-\frac{1}{x^2})$$ $$2(x^2-\frac{1}{x^2})$$ 

Answer 1

Given: 

${\displaystyle \cos ec\theta =2x,\cot \theta \frac{2}{x}}$ 

We know that, 

${\displaystyle \cos e{c}^2\theta -{\cot }^2\theta =1}$

⇒${\displaystyle {\left(2x\right)}^2-{\left(\frac{2}{x}\right)}^2=1}$ 

⇒${\displaystyle 4x^2-\frac{4}{x^2}=1}$ 

⇒ ${\displaystyle 4(x^2-\frac{1}{x^2})=1}$ 

⇒${\displaystyle 2\times 2\times (x^2-\frac{1}{x^2})=1}$ 

⇒ ${\displaystyle 2(x^2-\frac{1}{x^2})=\frac{1}{2}}$