trigonometrey~need major help!?

Question

find the exact value of cos 8° cos 38°+ sin 8°+ sin 38°

Answer 1

i assume that you actually meant
cos 8° * cos 38°+ sin 8° * sin 38°
not
cos 8° * cos 38°+ sin 8°+ sin 38°

you will notice that the two angles involved are the same:
8° and 38°

the expansion of cos (a + b)
is (cos a) * (cos b) - (sin a) * (sin b)

and this is almost what you have, when a = 38° and b = 8°, except you have a plus in the middle instead of a minus, so we must use at similar expansion

the expansion of cos (a - b)
is (cos a) * (cos b) + (sin a) * (sin b)
which is what you have when a = 38° and b = 8°

so cos 8° * cos 38°+ sin 8° * sin 38°
= cos (38° - 8°)
= cos 30°
= ( sqrt 3 ) / 2

so if my assumption that your equation was
cos 8° * cos 38°+ sin 8° * sin 38°
and not what you wrote in the question above, then your answer is
( sqrt 3 ) / 2

i dont think there is any easy way to find the exact value of what you wrote if that is correct

Answer 2

That's cos(8-38) = cos(-30) = cos(30) = √3/2

Answer 3

1.53517646341