Mimi_x3 one year ago Write the trigonometric expression as an algebraic expression in u and v. Assume that the variables u and v represent positive real numbers. $\cos(\sin^{−1}(u)-\tan^{−1}(v))$

1. dan815

okay so what exactly are we doing here

2. Mimi_x3

Im unsure myself =_=

3. dan815

you can always eliminate sin and cos with complex versions or power series

4. dan815

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5. dan815

you can try to figure out the inverse function here, for this complex version of sin and cos

6. dan815

you can also continue to write it in a power series if they prefer that

7. dan815

my last guess would be to start drawing triangles

8. dan815

since they have sin^-1(u) so

9. dan815

u can do the same to the other one

10. dan815

oh wait oops thats not right

11. dan815

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12. dan815

so ya i think we just gotta do make use of the cos(a-b) indentity

13. dan815

pretty simple from here, work it out

14. dan815

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15. 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)

16. dan815

cos(α – β) = cos(α)cos(β) + sin(α)sin(β)

17. Mimi_x3