Question

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

Answer 1

sin 2x

Explanation:

`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

1

Explanation:

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

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