How do you simplify $sin(sin^(-1)x + cos^(-1)x)$ ?

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Answer 1 · 2016-08-24T04:42:14

sin 2x

$sin^-1 x$ --> arcsin x --> arc x
$cos^-1 x$ --> arccos x --> arc x

$sin (sin^-1 x + cos^-1 x) = sin (x + x) = sin 2x$
Example.
$sin (arcsin (pi/6) + arccos (pi/6)) = sin (pi/6 + pi/6) = sin (pi/3)$

Answer 2 · 2016-08-24T05:53:45

1

As $sin^(-1)x + cos^(-1)x = pi/2$ ,

$sin(sin^(-1)x + cos^(-1)x) = sin (pi/2) = 1.$

How do you simplify sin(sin^(-1)x + cos^(-1)x)sin(sin^(-1)x + cos^(-1)x)?