Question

Rewrite sin(cos^-1x+sin^-1x) as an algebraic expression.

Answer 1

1
according to Mathematica.

Answer 2

how do they solve it? I am having trouble on where to begin...

Answer 3

use sum identity for sine

Answer 4

\[\sin^{-1} x+\cos^{-1} x=\frac{ \pi }{ 2 }\]

Answer 5

\[\sin \frac{ \pi }{ 2 }=1\]

Answer 6

\[put~\sin^{-1} x=t,x=\sin t=\cos \left( \frac{ \pi }{ 2 }-t \right)\]
\[or~\cos^{-1} x=\frac{ \pi }{ 2 }-t=\frac{ \pi }{ 2 }-\sin^{-1} x\]
\[or~\sin^{-1} x+\cos^{-1} x=\frac{ \pi }{ 2 }\]

Answer 7

Thanks , but I figured it out.

Answer 8

yw