Question

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

Answer 1

@dan815 @uri

Answer 2

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

Answer 3

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

Answer 4

@math1234 that would be correct

Answer 5

1/1+x^2 ?

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

Where x is your fractional expression above.

Answer 11

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

Answer 12

idk where to go from here

Answer 13

That's your answer.

Answer 14

Just add the denominator.

Answer 15

56/65
Refer to the attachment below.