Question

Is inverse $\sin$ the same as $cosec$?

Answer 1

Determine if inverse $\sin$ is the same as $cosec$

Inverse $\sin$ is written as: ${\sin }^{-1}\left(x\right)$

If $x=\sin \left(y\right),\text{then}y={\sin }^{-1}\left(x\right)$.

Whereas, $csc$ is the reciprocal of $\sin$ and is written as: $\csc \left(x\right)=\frac{1}{\sin \left(x\right)}$

It can also be written as: $\csc \left(x\right)={\left(\sin \left(x\right)\right)}^{-1}$

It is evident that the inverse of a function is different from the reciprocal of the function.

Therefore, inverse $\sin$ is not the same as $cosec$.