Question

Help please!
Find an algebraic expression equivalent to the following expressions:
cos(tan^-1 x)


cot(arcsin x)

Answer 1

@jim_thompson5910 can you help ?

Answer 2

hmmm, do you recall the ranges for inverse trig functios?
that is \(\textit{Inverse Trigonometric Identities}
\\ \quad \\

\begin{array}{cccl}

Function&{\color{brown}{ Domain}}&{\color{blue}{ Range}}\\
\hline\\
{\color{blue}{ y}}=sin^{-1}({\color{brown}{ \theta}})&-1\le {\color{brown}{ \theta}} \le 1&-\frac{\pi}{2}\le {\color{blue}{ y}}\le \frac{\pi}{2}
\\ \quad \\
{\color{blue}{ y}}=cos^{-1}({\color{brown}{ \theta}})&-1\le {\color{brown}{ \theta}} \le 1& 0 \le {\color{blue}{ y}}\le \pi
\\ \quad \\
{\color{blue}{ y}}=tan^{-1}({\color{brown}{ \theta}})&-\infty\le {\color{brown}{ \theta}} \le +\infty &-\frac{\pi}{2}\le {\color{blue}{ y}}\le \frac{\pi}{2}
\end{array}\)

Answer 3

yes

Answer 4

\[put~\tan^{-1} x=y,x=\tan y\]