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exact value

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1 Answer

tanβ = sinβ / cosβ ,
sin450 = cos450 = (√2)/2 ---> tan450 = 1
sin300 = 1/2 , cos300 = √3 / 2 ---> tan300 = 1/√3

tan(450 + 300) = (tan45 + tan30) / (1 - tan45·tan30) = (1 + 1/√3) / (1 - 1/√3) =
(√3 + 1) · (√3 + 1)        (√3 + 1)2         (√3)2 + 2√3 + 1 
 (√3 - 1) · (√3 + 1)        (√3)2 - 12                  2   

  2(2 + √3)                2 + √3   <----- is the final answer
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