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Evaluate cot2(75°). please help

Guest Feb 14, 2017
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cot^2(75°)

 

Note.....  csc^2(75°)   =  1 + cot^2(75°)      →  csc^2(75°)  - 1  = cot^2(75°)

 

sin(75°) = sin(30 + 45)  =  sin30cos45 + sin45cos30  =

 

(1/2) * sqrt(2)/2  + sqrt (2)/2  * sqrt (3)/2  =

 

sqrt (2) / 4  +  sqrt (6) / 4

 

 

sin^2(75°)  =  [sqrt (2) / 4  +  sqrt (6) / 4] =  2/16 + 2sqrt(12)/16 + 6/16  =

 

1/2  + sqrt(12)/8   =  (1/2   + 2sqrt(3) / 8 )  =  1/2 + sqrt(3)/4   =  [2 + sqrt(3)] / 4

 

1 / sin^2(75°) =    1 /  [ (2 + sqrt(3) ) / 4]  =       4 /  [ 2 + sqrt(3)] =

 

[4 * (2 - sqrt(3)) ] /  (  2 + sqrt(3) *  (2 - sqrt(3) ]  =  

 

[4 * (2 - sqrt(3)) ]  / [ 4 - 3 ]  = 

 

8 - 4sqrt (3)    = csc^2(75°)

 

csc^2(75°)  - 1  = cot^2(75°)

 

8 - 4sqrt (3) - 1  = cot^2(75°)

 

7 - 4sqrt (3)   = cot^2(75°)

 

 

cool cool cool

CPhill  Feb 14, 2017

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