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.#