Write each of the following in the simplest form:(i) cot-1ax2-a2, x >a(ii) tan-1x+1+x2, x∈R(iii) tan-11+x2-x, x∈R(iv) tan-11+x2-1x, x≠0(v) tan-11+x2+1x, x≠0(vi) tan-1a-xa+x,-a<x<a(vii) tan-1xa+a2-x2,-a<x<a(viii) sin-1x+1-x22,-1<x<1(ix) sin-11+x+1-x2, 0<x<1(x) sin2 tan-11-x1+x

Write each of the following in the simplest form:(i) cot-1ax2-a2, x

1.	Write each of the following in the simplest form:(i) cot-1ax2-a2, x >a(ii) tan-1x+1+x2, x∈R(iii) tan-11+x2-x, x∈R(iv) tan-11+x2-1x, x≠0(v) tan-11+x2+1x, x≠0(vi) tan-1a-xa+x,-a<x<a(vii) tan-1xa+a2-x2,-a<x<a(viii) sin-1x+1-x22,-1<x<1(ix) sin-11+x+1-x2, 0<x<1(x) sin2 tan-11-x1+x
Answer» Write each of the following in the simplest form: (i) $\cot^{- 1} \frac{a}{\sqrt{x^{2} - a^{2}}}, \|x\| > a$ (ii) $\tan^{- 1} \{x + \sqrt{1 + x^{2}}\}, x \in R$ (iii) $\tan^{- 1} \{\sqrt{1 + x^{2}} - x\}, x \in R$ (iv) $\tan^{- 1} \{\frac{\sqrt{1 + x^{2}} - 1}{x}\}, x \neq 0$ (v) $\tan^{- 1} \{\frac{\sqrt{1 + x^{2}} + 1}{x}\}, x \neq 0$ (vi) $\tan^{- 1} \sqrt{\frac{a - x}{a + x}}, - a < x < a$ (vii) $\tan^{- 1} \{\frac{x}{a + \sqrt{a^{2} - x^{2}}}\}, - a < x < a$ (viii) $\sin^{- 1} \{\frac{x + \sqrt{1 - x^{2}}}{\sqrt{2}}\}, - 1 < x < 1$ (ix) $\sin^{- 1} \{\frac{\sqrt{1 + x} + \sqrt{1 - x}}{2}\}, 0 < x < 1$ (x) $\sin \{2 \tan^{- 1} \sqrt{\frac{1 - x}{1 + x}}\}$