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Sona
 3 years ago
how wud u solve the following?
\[\cos (\tan^{1} (5/12)+\tan^{1} (15/8))\]
Plz help this is in 15 min!
Sona
 3 years ago
how wud u solve the following? \[\cos (\tan^{1} (5/12)+\tan^{1} (15/8))\] Plz help this is in 15 min!

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cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0ok do the numbers (5,12, ) and (8,15, ) remind you of something?

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0these numbers appear in the problem for good reason

Sona
 3 years ago
Best ResponseYou've already chosen the best response.0umm im not sure way u mean

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

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0pythagorean triples. i.e. integer side lengths for right triangles

Sona
 3 years ago
Best ResponseYou've already chosen the best response.0ok then wat do i do w/this #?

Sona
 3 years ago
Best ResponseYou've already chosen the best response.0don't mean to rush but this is due online in 10 min exactly

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0so 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

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0ugh sry not familiar with the mathtype syntax here... i apologize for poorly formatted equations

Sona
 3 years ago
Best ResponseYou've already chosen the best response.0its ok don't worry bout its understandable

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0now 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

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0draw your triangles, and identify which angle is a, and which angles is b

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0now 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)

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

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

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0sry, diagram not drawn to scale

Sona
 3 years ago
Best ResponseYou've already chosen the best response.0thats fine but I'm still stuck :(

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0ok 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)

cnknd
 3 years ago
Best ResponseYou've already chosen the best response.0now 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)

akinfermo
 3 years ago
Best ResponseYou've already chosen the best response.0you should make a change of variables
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