Question

@AZ healp

Answer 1

Like, I need a way to do this without using a calculator

Answer 2

This is going to be a long one lool

\( \cos (a - b) = \cos (a) \cos (b) + \sin (a) \sin (b)\)

Answer 3

Some tools:
https://www.dummies.com/education/math/calculus/how-to-calculate-the-cosine-of-an-angle/
https://www.dummies.com/education/math/calculus/how-to-calculate-the-tangent-of-an-angle/#:~:text=Follow%20these%20steps%3A%201%20Draw%20a%20diagram%20that,get%20x%20tan%2080%20degrees%20%3D%2039.%20

Answer 4

So should I plug all of htat in o-o

Answer 5

Have you learned the inverse trigonometric functions yet?

Answer 6

AZ, I'll leave the post to you, I am not that equipped to help with trig...

Answer 7

Well if they're asking you this question, then you're expected to know it hmm

Answer 8

If it is a site like edgenuity, they sometimes exclude stuff or put questions on the wrong assignments. I might flag that problem to your teacher so that it can be resolved

Answer 9

But btw for the thingy
\[[\cos(\tan ^{-1}\frac{ 5 }{ 12 })][\cos(\cos ^{-1}\frac{ 4 }{ 5 })] + [\sin(\tan ^{-1}\frac{ 5 }{ 12 })][\sin(\cos ^{-1}\frac{ 4 }{ 5 })]\]

Answer 10

so obviously

\( \cos (\cos^{-1} x) = x\)

and then use the formulas in that screenshot

Answer 11

ye, give me a moment xd

Answer 12

\[(\frac{ 1 }{ \sqrt(1+\frac{ 25 }{ 144 }) })(\frac{ 4 }{ 5 })+(\frac{ \frac{ 4 }{ 5 } }{ \sqrt(1+\frac{ 16 }{ 25 }) })(\sqrt(1-\frac{ 16 }{ 25 })\]

Answer 13

And then that would simplify to
\[\frac{ 1 }{\sqrt( \frac{ 169 }{ 144 }) }(\frac{ 4 }{ 5 })+(\frac{ \frac{ 4 }{ 5 } }{ \sqrt(\frac{ 41 }{ 25 }) })(\sqrt \frac{ 9 }{ 25 }\]

Answer 14

not simplify more like-, change to

Answer 15

which and then goes to
\[(\frac{ 1 }{ \frac{ 13 }{ 12 } })(\frac{ 4 }{ 5 })+(\frac{ 4 }{ 5 })(\frac{ 1 }{ \sqrt(\frac{ 41 }{ 25 } )})(\frac{ 3 }{ 5 })\]

Answer 16

and i could simplify the rest but how woudl i get rid of hte sqrt41/25

Answer 17

\[ \left(\frac{ 1 }{ \sqrt{1+\frac{ 25 }{ 144 }} }\right) \left(\frac{ 4 }{ 5 }\right) +\left(\frac{ \frac{ 4 }{ 5 } }{ \sqrt(1+\color{red}{\frac{ 25 }{ 144 }}) }\right)\left(\sqrt{1-\frac{ 16 }{ 25 }}\right)\]

Answer 18

oh

Answer 19

ohhhh oopsssssssssss

Answer 20

So it would be
\[(\frac{ 12 }{ 13 })(\frac{ 4 }{ 5 }) + (\frac{ 4 }{ 5 })(\frac{ 12 }{ 13 })(\frac{ 3 }{ 5 })\]

Answer 21

\[ \left(\frac{ 1 }{ \sqrt{1+\frac{ 25 }{ 144 }} }\right) \left(\frac{ 4 }{ 5 }\right) +\left(\frac{ \frac{ 4 }{ 5 } }{ \sqrt{1+\frac{ 25 }{ 144 }} }\right)\left(\sqrt{1-\frac{ 16 }{ 25 }}\right)\]


\[ \left(\frac{ 1 }{\dfrac{13}{12} }\right) \left(\frac{ 4 }{ 5 }\right) +\left(\frac{ \frac{ 4 }{ 5 } }{ \dfrac{13}{12} }\right)\left(\dfrac{3}{5}\right)\]

Answer 22

and tehn i got
384/225?

Answer 23

not 225

Answer 24

oh oops

Answer 25

okay done

thankssssssssssssssssssssssssssssssssssssss so much xd

Answer 26

You're welcome!

Answer 27

wdym

Answer 28

\[ \left(\frac{ 1 }{ \sqrt{1+\frac{ 25 }{ 144 }} }\right) \left(\frac{ 4 }{ 5 }\right) +\left(\frac{ \frac{ 5 }{ 12 } }{ \sqrt{1+\frac{ 25 }{ 144 }} }\right)\left(\sqrt{1-\frac{ 16 }{ 25 }}\right)\]


\[ \left(\frac{ 1 }{\dfrac{13}{12} }\right) \left(\frac{ 4 }{ 5 }\right) +\left(\frac{ \frac{ 5 }{ 12 } }{ \dfrac{13}{12} }\right)\left(\dfrac{3}{5}\right)\]

Answer 29

so

(12/13 * 4/5) + (5/12 * 12/13 * 3/5)

Answer 30

so i got
756/780

Answer 31

nope nope, do it again

you'll get the answer you shared in DMs with me

Answer 32

oh, it simplifies to that 63/65 lol

Answer 33

exactly

Answer 34

xddd thanksssssssss