Basic Concepts

Find the principal value of ${\tan }^{-1}\sqrt{3}-{\sec }^{-1}(-2)$.

If ${\sin }^{-1}x=y,$ then

${\tan }^{-1}\sqrt{3}-{\cot }^{-1}(-\sqrt{3})$ is equal to

The value of $\sin \left(\frac{\pi }{3}-{\sin }^{-1}\left(-\frac{1}{2}\right)\right)$ is equal to

The value of ${\cos }^{-1}\left(\cos \frac{7\pi }{6}\right)$ is equal to

Find the value of ${\mathrm{t}\mathrm{a}\mathrm{n}}^{-1}\left(\tan \frac{7\pi }{6}\right)$

Find the value of ${\cos }^{-1}\left(\cos \frac{13\pi }{6}\right)$

Find the value of ${cos}^{-1}\left(\frac{1}{2}\right)+2{sin}^{-1}\left(\frac{1}{2}\right)$.

Find the value of ${tan}^{-1}\left(1\right)+{cos}^{-1}\left(-\frac{1}{2}\right)+{sin}^{-1}\left(-\frac{1}{2}\right)$.

Find the principal value of ${\mathrm{cosec}}^{-1} \left(-\sqrt{2}\right)$.

Find the principal value of ${cos}^{-1}\left(-\frac{1}{\sqrt{2}}\right)$.

Find the principal value of ${\cot }^{-1}\left(\sqrt{3}\right)$.

Find the principal value of ${sec}^{-1}\left(\frac{2}{\sqrt{3}}\right)$

Find the principal value of ${tan}^{-1}\left(-1\right)$

Find the principal value of ${cos}^{-1}\left(-\frac{1}{2}\right)$

Find the principal value of $ta{n}^{-1}\left(-\sqrt{3}\right)$

Find the principal value of ${\mathrm{cosec}}^{-1} \left(2\right)$.

Find the principal value of ${\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Find the principal value of ${\sin }^{-1}\left(-\frac{1}{2}\right)$