Write the `tan^-1 (frac{x^2}{ a^2-x^2)),|x| < a`. in the simplest form.

Write the tan^-1 (frac{cos x}{1+sin x}), -frac{pi}{2} < x < frac {pi}{2} in the simplest form.

Write the tan^-1 (frac{3a^2 x-x^3}{a^3- 3 ax^2)), a>0,- frac {a}{ 3} le x le frac{a}{ 3} . in the simplest form.

Write the cot^-1 (frac {1}{ sqrt(x^2 -1) }), |x| > 1 . in the simplest form.

Write the tan^-1 (frac{cos x - sin x}{cos x + sin x)), x < pi . in the simplest form.

Write the following function in the simplest form: tan^-1 (x/sqrt(a^2 - x^2)), |x|

Show that: tan^-1 (frac {1-x}{1+x})= frac {1}{2} tan^-1(frac{1-x^2}{2x}), x>0

Write tan^-1( sqrt (frac {1-cos x}{1+cos x})) , x < pi in the simplest form.

Sum the series tan^-1 frac{1}{1+1+1^2} + tan^-1 frac{1}{1+2+2^2} + tan^-1 frac{1}{1+3+3^2} + …...... To oo .

Prove that : 2 tan^-1 frac{1}{2} + tan^-1 frac{1}{7}=tan^-1 frac{31}{17}

Write tan^(-1)((1)/(sqrt(x^(2)-1))),|x|gt1 in simplest form.