Question

Write the given expression in terms of x and y only. cos(arcsin x − arctan y)

Answer 1

let a=arcsin(x) and b=arctan(y)

Answer 2

cos(a-b) equals what in terms of cos(a),cos(b),sin(a), and sin(b)

Answer 3

use the difference identity for cosine that is

Answer 4

now for sin(a)=x and tan(b)=y
we are going to build two separate right triangles

Answer 5

sin(a)=x/1
so for this triangle you will label the side opp of angle a x
and hyp 1

-----
tan(b)=y/1
so for this triangle you will label the side opp of angle b y
and the adjacent side of angle b 1

Answer 6

you should find the other unknown side in both triangles

Answer 7

you will use this info write cos(a-b) as an algebraic expression

Answer 8

my answer didnt work for that

Answer 9

have you expanded cos(a-b) using the difference identity?

Answer 10

yes unless i did the math wrong, but i used cosacosb+sinasinb and tried to simplify after that

Answer 11

\[\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)\]
that is correct
and we have this also