$\int_{\cos\,\cos^{-1}α}^{\sin\,\sin^{-1}β}|\frac{\cos(\cos^{-1}x)}{\sin(\sin^{-1}x)}|dx(α,β∈[0,1])$ is equal to:

1 1/2 $β-α$ None of these

$β-α$

As we have $\sin^{-1}β$ and $\cos^{-1}α$ defined, If $α,β∈[0,1]$ $\cos(\cos^{-1})=x\,∀\,x∈[-1,1];\sin(\sin^{-1})=x\,∀\,x∈[-1,1]$ $\int\limits_{\cos\,\cos^{-1}α}^{\sin\,\sin^{-1}β}|\frac{\cos(\cos^{-1}x)}{\sin(\sin^{-1}x)}|dx=\int\limits_{α}^{β}1dx=β-α$