Evaluate a trigonometry problem, help please?

Question

Evaluate cos(arctan(3/4) - arcsin(1/3)) withou using a calculator (exact values)


please show step by step if you can so i can try to follow along, thank you

Answer 1

tan a=3/4
cosa=4/5
sina= 3/5

sin b=1/3
cosb=2sqrt(2)/3

cos(a-b)=cosacosb+sinasinb
=4/5*2sqrt(2)/3+3/5*1/3

Answer 2

cos(arctan(3/4)- arcsin(1/3)) =
the hypotenuse of arc tangent 3/4 is 5, therefore the cosine is 4/5.
The angle of arc sin (1/3) has a leg of b= to square root of (9-1) or b = 2 (square root of 2)/3
Therefore:
Cos(arctangent 3/4- arc sin(1/3)=
cos arctan(3/4) -cos (arcsin (1/3)=
4/5 -2(square root of 2)/3=
12/15) - 10(square of 2)/15=
(12-14.14)/15