Find the exact value of the expression cos(sin^-15/13-tan^-14/3)

Answer 1

Draw your right triangles. If we let
sinx = -15/13
tany = -14/3
then assuming the principal values of the inverse trig functions,
cosx = √56/13
siny = -14/√205
cosy = 3/√205
and finally,
cos(x-y) = cosx cosy + sinx siny
= √56/13 * 3/√205 + 15/13 * 14/√205
= (3√56 + 210)/(13√205)

Answer 2

One small problem:
sinx = -15/13 <----- not possible

oobleck read sin^-15/13-tan^-14/3
as
sin^-1 (-15/13) - tan^-1 (-14/3)
instead of sin^-1 (5/13) - tan^-1 (4/3)

now we are dealing with the 5-12-13 and 3-4-5 triangles and the
calculations become easier.

Answer 3

nice catch, Reiny. I thought that 13,15 combination was weird.
No doubt Ashlyn caught my mis-reading and adjusted her steps accordingly ...