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 Cot Ratio Conclusion (Posted on 2014-10-18)
BC, CA and AB represents three sides of a triangle having lengths a, b and c respectively. Angles A, B and C are opposite respectively to the sides BC, CA and AB

Given that: a2 + b2= 2015* c2

Find the value of :
```   cot  C
-------------
cot A + cot B```

 No Solution Yet Submitted by K Sengupta No Rating

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 Solution Comment 2 of 2 |
a2 + b2 = 2015c2 and the rule c2 = a2 + b2 – 2ab*cos C,

together give:  ab*cos C =1007c2.                                   (1)

cot C                      sin A * sin B * cot C
---------------      =    ----------------------------------
cot A + cot B            sin B * cos A  +  sin A * cos B

sin A * sin B * cos C
=    --------------------------
sin C * sin(A + B)

sin A * sin B * cos C
=    --------------------------               (2)
sin2C

Now, since   a/sin A = b/sin B = c/sin C, (2) becomes

cot C
---------------      =   ab*cos C / c2  =  1007       using (1)
cot A + cot B

 Posted by Harry on 2014-10-22 18:05:57

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