## Sona Group Title how wud u solve the following? $\cos (\tan^{-1} (-5/12)+\tan^{-1} (15/8))$ Plz help this is in 15 min! one year ago one year ago

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1. cnknd Group Title

ok do the numbers (5,12, ) and (8,15, ) remind you of something?

2. cnknd Group Title

these numbers appear in the problem for good reason

3. Sona Group Title

umm im not sure way u mean

4. cnknd Group Title

ok let me fill in the blanks: (5,12,13), (8,15,17). do these numbers look familiar?

5. Sona Group Title

these r (x y r) values?

6. cnknd Group Title

pythagorean triples. i.e. integer side lengths for right triangles

7. Sona Group Title

ok then wat do i do w/this #?

8. Sona Group Title

don't mean to rush but this is due online in 10 min exactly

9. cnknd Group Title

so you know [\tan^{-1} (-5/12)] refers to the 5,12,13 triangle, and [\tan^{-1} (15/8)] refers to the 8,15,17 triangle

10. cnknd Group Title

ugh sry not familiar with the mathtype syntax here... i apologize for poorly formatted equations

11. Sona Group Title

its ok don't worry bout its understandable

12. cnknd Group Title

now the 2 inverse tangents give you to angles. let's call them a and b. the angle a comes from the 5,12,13 triangle, and the angle b comes from the 8,15,17 triangle

13. cnknd Group Title

draw your triangles, and identify which angle is a, and which angles is b

14. cnknd Group Title

now back at the original equation, since i'm lazy and don't want to write out all the inverse tangents, i'll just write a and b: cos(a+b) = cos(a) cos(b) - sin(a) sin(b)

15. cnknd Group Title

from your triangles, you should be able to identify what cos(a), cos(b), sin(a), and sin(b) are

16. Sona Group Title

so y for the 1st one is 5 n x is 12 while the 2nd y is 15 n 2nd x is 8?

17. cnknd Group Title

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18. cnknd Group Title

sry, diagram not drawn to scale

19. Sona Group Title

thats fine but I'm still stuck :(

20. cnknd Group Title

ok back to original equation remember a = tan-1(5/12) and b = tan-1(15/8) so the original equation: cos(a+b), can be expanded as cos(a)cos(b) - sin(a)sin(b)

21. cnknd Group Title

now look at the pictures, what's cos(a)? what's cos(b)? what's sin(a)? what's sin(b)? (remember cos is adjacent/hypotenuse, sin is opposite/hypotenuse)

22. akinfermo Group Title

you should make a change of variables