give the exact real number value without using a calculator

Question

sin[(cos^-1)(1/4)]

sin[(tan^-1)(3/4)+(tan^-1)(12/5)]

Answer 1

On each of these, draw the triangle. On the first, the adjacent side is 1, the hyp is 4, so the opposite side is sqrt(16-1) So sine of that angle is sqrt15/4

Same idea on the next.