cos(arcsin(x)+arctan(x))

Answer 1

Let arcsin(x) = A
let arctan(x) = B

then cos(arcsin(x) + arctan(x))
= cos(A+B)
= cosAcosB - sinAsinB **

from arcsin(x) = A
sinA = x/1
cosA = √(1-x^2) , using Pythagoras

from arctan(x) = B
tanB = x/1 ,
then sinB = x/√(x^2 + 1)
cosB = 1/√(x^2 + 1)

back into **

cosAcosB - sinAsinB
= √(1 - x^2) (1/√(x^2 + 1) - (x/1)(x/√(x^2 + 1)
= ( √(1 - x^2) - x^2 )/(√(x^2 + 1) )

check my typing, should have written it out first.