Write the trigonometric expression as an algebraic expression in u and v. Assume that the variables u and v represent positive real numbers. \[\cos(\sin^{−1}(u)-\tan^{−1}(v))\]

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Write the trigonometric expression as an algebraic expression in u and v. Assume that the variables u and v represent positive real numbers. \[\cos(\sin^{−1}(u)-\tan^{−1}(v))\]

Mathematics
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okay so what exactly are we doing here
Im unsure myself =_=
you can always eliminate sin and cos with complex versions or power series

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Other answers:

|dw:1443141313790:dw|
you can try to figure out the inverse function here, for this complex version of sin and cos
you can also continue to write it in a power series if they prefer that
my last guess would be to start drawing triangles
since they have sin^-1(u) so
u can do the same to the other one
oh wait oops thats not right
|dw:1443141590469:dw|
so ya i think we just gotta do make use of the cos(a-b) indentity
pretty simple from here, work it out
|dw:1443142431740:dw|
=cos(sin^-1(u))*cos(tan^-1(v)) + sin(sin^-1(u)) sin(tan^-1(v)) =sqrt(1-u^2)*1/sqrt(1+u^2) + u* v/sqrt(1+v^2)
cos(α – β) = cos(α)cos(β) + sin(α)sin(β)
Thanks @dan815 My page kept reloading

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