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{cos x - sin x}{cos x + sin x)), x < pi . in the simplest form.

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

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

Prove that : sin^-1 frac{5}{13} + sin^-1 frac{7}{25}= cos^-1 frac{253}{325}

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

2tan^-1 frac{1}{3} + tan^-1 frac{1}{7}= frac {pi}{4}

Prove that : sin^-1 (frac{5}{13}) + cos^-1 (frac{4}{5}) = frac{1}{2} sin^-1 (frac {3696}{4225}) .

Solve for x: tan^-1 (frac{x}{2}) + tan^-1(frac{x}{3}) = frac{pi}{4}, x > 0

tan^-1 frac{1}{2} + tan^-1 frac{2}{11}= frac{1}{2}sin^-1 frac{24}{25}