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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
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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cnkndBest ResponseYou've already chosen the best response.0
ok do the numbers (5,12, ) and (8,15, ) remind you of something?
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
these numbers appear in the problem for good reason
 one year ago

SonaBest ResponseYou've already chosen the best response.0
umm im not sure way u mean
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
ok let me fill in the blanks: (5,12,13), (8,15,17). do these numbers look familiar?
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
pythagorean triples. i.e. integer side lengths for right triangles
 one year ago

SonaBest ResponseYou've already chosen the best response.0
ok then wat do i do w/this #?
 one year ago

SonaBest ResponseYou've already chosen the best response.0
don't mean to rush but this is due online in 10 min exactly
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
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
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
ugh sry not familiar with the mathtype syntax here... i apologize for poorly formatted equations
 one year ago

SonaBest ResponseYou've already chosen the best response.0
its ok don't worry bout its understandable
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
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
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
draw your triangles, and identify which angle is a, and which angles is b
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
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)
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
from your triangles, you should be able to identify what cos(a), cos(b), sin(a), and sin(b) are
 one year ago

SonaBest ResponseYou've already chosen the best response.0
so y for the 1st one is 5 n x is 12 while the 2nd y is 15 n 2nd x is 8?
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
sry, diagram not drawn to scale
 one year ago

SonaBest ResponseYou've already chosen the best response.0
thats fine but I'm still stuck :(
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
ok back to original equation remember a = tan1(5/12) and b = tan1(15/8) so the original equation: cos(a+b), can be expanded as cos(a)cos(b)  sin(a)sin(b)
 one year ago

cnkndBest ResponseYou've already chosen the best response.0
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)
 one year ago

akinfermoBest ResponseYou've already chosen the best response.0
you should make a change of variables
 one year ago
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