Mimi_x3
  • Mimi_x3
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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dan815
  • dan815
okay so what exactly are we doing here
Mimi_x3
  • Mimi_x3
Im unsure myself =_=
dan815
  • dan815
you can always eliminate sin and cos with complex versions or power series

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dan815
  • dan815
|dw:1443141313790:dw|
dan815
  • dan815
you can try to figure out the inverse function here, for this complex version of sin and cos
dan815
  • dan815
you can also continue to write it in a power series if they prefer that
dan815
  • dan815
my last guess would be to start drawing triangles
dan815
  • dan815
since they have sin^-1(u) so
dan815
  • dan815
u can do the same to the other one
dan815
  • dan815
oh wait oops thats not right
dan815
  • dan815
|dw:1443141590469:dw|
dan815
  • dan815
so ya i think we just gotta do make use of the cos(a-b) indentity
dan815
  • dan815
pretty simple from here, work it out
dan815
  • dan815
|dw:1443142431740:dw|
dan815
  • dan815
=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)
dan815
  • dan815
cos(α – β) = cos(α)cos(β) + sin(α)sin(β)
Mimi_x3
  • Mimi_x3
Thanks @dan815 My page kept reloading

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