List of top Mathematics Questions on Inverse Trigonometric Functions

Solution of sinx + sin5x = sin 3x in (0,ℼ/2) are..?

The principal value of sin-1(sin 3ℼ/4) is?

Solve for x, given tan-1 (1 - x/1 + x) = ½ tan-1x

If
\(0 < x< \frac{1}{\sqrt2}\ and\ \frac{\sin^{-1}x}{α} = \frac{\cos^{-1}x}{β} \)
then a value of 
\(sin(\frac{2πα}{α+β}) \)
is

For k ∈ R, let the solution of the equation
\(\cos\left(\sin^{-1}\left(x \cot\left(\tan^{-1}\left(\cos\left(\sin^{-1}\right)\right)\right)\right)\right) = k, \quad 0 < |x| < \frac{1}{\sqrt{2}}\)
Inverse trigonometric functions take only principal values. If the solutions of the equation x² – bx – 5 = 0 are
\(\frac{1}{α^2}+\frac{1}{β^2} \)and \(\frac{α}{β}\)
, then b/k2 is equal to_____.

\(\tan⁡(2\tan^{−1}\frac{⁡1}{5}+\sec^{−1}⁡\frac{\sqrt5}{2}+2\tan^{−1}⁡\frac{1}{8})\)
is equal to :

The value of 
\(\lim_{{n \to \infty}} 6\tan\left\{\sum_{{r=1}}^{n} \tan^{-1}\left(\frac{1}{{r^2+3r+3}}\right)\right\}\)
is equal to :

With reference to the principal values, if sin^-1x + sin^-1y + sin^-1z = \(\frac {3π}{2}\), then x¹⁰⁰ + y¹⁰⁰ + z¹⁰⁰ =?