## anonymous one year ago cos(arctan(-12/5)+arctan(3/4))

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1. anonymous

@dan815 @uri

2. anonymous

I'm assuming that you want to solve this in exact form by hand without a calculator.

3. anonymous

In that case, you will need to use the arctan sum formula.

4. anonymous

@math1234 that would be correct

5. anonymous

1/1+x^2 ?

6. anonymous

No, it is $\tan^{-1} a + \tan^{-1} b = \tan^{-1} \frac{ a+b }{ 1-ab }$

7. anonymous

Upon combining the inside using the arctan sum formula, you can use your mentioned formula to compute the cos of the arctan.

8. anonymous

so that gves us $\tan^{-1} \frac{ \frac{ -12 }{ 5 }+\frac{ 3 }{ 4 } }{ 1-\frac{ -12 }{ 4 }*\frac{ 3 }{ 4 } }$

9. anonymous

Yes, then you plug it into $\cos (\tan^{-1} x) = \frac{ 1 }{ \sqrt{1+x^2} }$

10. anonymous

Where x is your fractional expression above.

11. anonymous

$\cos (\tan^{-1} \frac{ 33 }{ 16 })=\frac{ 1 }{ \sqrt{1+(\frac{ 33 }{ 6 }})^{2} }$

12. anonymous

idk where to go from here

13. anonymous

14. anonymous