Question

How do you find the exact value of `Sin(arcsin(1/3)-arcsin(1/4))`?

Answer 1

`1/12(sqrt15-2sqrt2)=0.0870`, nearly.

Explanation:

Use `sin (a-b)=sin a cos b - cos a sin b and f f^(-1)(y) = y.` and, for x in

`Q_1`, cos x = sqrt(1-sin^2 x) and, likewise, sin x = sqrt( 1-cos^2x)#

The given expression becomes

`sin arcsin(1/3)cos sin arc sin (1/4)-cos arc sin (1/3) sin arc arc sin (1/4)`

`=1/3cos arc cos sqrt(1-(1/4)^2)-1/4cos arc cossqrt(1-(1/3)^2)`

`=1/3sqrt(1-1/16)-1/4sqrt(1-1/9)`

`1/12(sqrt15-2sqrt2)`.