SOLUTION: How do I write the following trigonometric expression as an algebraic expression containing 'u' and 'v'? csc(arctan(u)+arccos(v))

Question 729314: How do I write the following trigonometric expression as an algebraic expression containing 'u' and 'v'?
csc(arctan(u)+arccos(v))
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
How do I write the following trigonometric expression as an algebraic expression containing 'u' and 'v'?
csc(arctan(u)+arccos(v))
***
let O=opposite side
let A=adjacent side
let H=hypotenuse
..
(arctan(u)=angle x
u=O/A=u/1
O=u, A=1
H=√(O^2+A^2)=√(u^2+1^1)=√(u^2+1)
cosx=A/H=1/√(u^2+1)
sinx=O/H=u/√(u^2+1)
..
arccos(v)=angle y
v=A/H=v/1
A=v, H=1
O=√(H^2+A^2)=√(1^2+v^2)=√(1+v^2)
cosy=A/H=v
siny=O/H=√(1+v^2)
..
csc(arctan(u)+arccos(v))=csc(x+y)=1/sin(x+y)
Identity: sin(x+y)=sinxcosy+cosxsiny=[u/√(u^2+1)]*v+[1/√(u^2+1)*√(1+v^2)]
csc(arctan(u)+arccos(v))=1/{[u/√(u^2+1)]*v+[1/√(u^2+1)*√(1+v^2)]}

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