cos(arctan(-12/5)+arctan(3/4))

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cos(arctan(-12/5)+arctan(3/4))

Trigonometry
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I'm assuming that you want to solve this in exact form by hand without a calculator.
In that case, you will need to use the arctan sum formula.

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Other answers:

@math1234 that would be correct
1/1+x^2 ?
No, it is \[\tan^{-1} a + \tan^{-1} b = \tan^{-1} \frac{ a+b }{ 1-ab }\]
Upon combining the inside using the arctan sum formula, you can use your mentioned formula to compute the cos of the arctan.
so that gves us \[\tan^{-1} \frac{ \frac{ -12 }{ 5 }+\frac{ 3 }{ 4 } }{ 1-\frac{ -12 }{ 4 }*\frac{ 3 }{ 4 } }\]
Yes, then you plug it into \[\cos (\tan^{-1} x) = \frac{ 1 }{ \sqrt{1+x^2} }\]
Where x is your fractional expression above.
\[\cos (\tan^{-1} \frac{ 33 }{ 16 })=\frac{ 1 }{ \sqrt{1+(\frac{ 33 }{ 6 }})^{2} }\]
idk where to go from here
That's your answer.
Just add the denominator.
56/65 Refer to the attachment below.

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