The value of $$\sin \left(\cot ^{-1} x\right)$$ is

If $$\cos ^{-1} \sqrt{\mathrm{p}}+\cos ^{-1} \sqrt{1-\mathrm{p}}+\cos ^{-1} \sqrt{1-\mathrm{q}}=\frac{3 \pi}{4}$$, then $$\mathrm{q}$$ is

$$\pi+\left(\sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}\right)$$ is equal to

If $$\alpha=3 \sin ^{-1} \frac{6}{11}$$ and $$\beta=3 \cos ^{-1}\left(\frac{4}{9}\right)$$, where the inverse trigonometric functions take only the principal values, then the correct option is