How do you evaluate tan(arcsin(3/4)-arccos(1/3))?

1 Answer
Apr 9, 2016

(3-2sqrt14)/(sqrt7+6sqrt2)=-0.4028. nearly.

Explanation:

If a = arc sin(3/4), sin a = 3/4 and tan a =3/sqrt7.
If b = arc cos(1/3), cos b = 1/3 and tan b = 2sqrt2
The given expression is
tan(a-b)=(tan a-tan b)/(1+tan a tan b)=(3/sqrt7-2sqrt2)/(1+6sqrt2/sqrt7)=(3-2sqrt14)/(sqrt7+6sqrt2).