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標題:
f.4 a.math.. compound angle
發問:
given that A and B are the roots of the equation tan^2 x - 3surd3 tan x + 1 =0 where A and B are acute angles with A
最佳解答:
By the relation between roots and coefficients, tan A + tan B =3surd 3 and tan A tan B =1 cot (A-B) =1/tan(A-B) =(1+tanA tanB)/(tanA- tanB) tan A + tan B =3srd 3 tan^2 A +2tan A tanB + tan^2 B= 27 tan^2 A -2tan A tanB +tan^2 = 23 (tan A-tanB)^2=23 tan A - tan B =-sqrt 23 so (1+tanA tanB)/(tanA- tanB) =(1+1)/-(sqrt23) =-2 sqrt 23
f.4 a.math.. compound angle
發問:
given that A and B are the roots of the equation tan^2 x - 3surd3 tan x + 1 =0 where A and B are acute angles with A
最佳解答:
By the relation between roots and coefficients, tan A + tan B =3surd 3 and tan A tan B =1 cot (A-B) =1/tan(A-B) =(1+tanA tanB)/(tanA- tanB) tan A + tan B =3srd 3 tan^2 A +2tan A tanB + tan^2 B= 27 tan^2 A -2tan A tanB +tan^2 = 23 (tan A-tanB)^2=23 tan A - tan B =-sqrt 23 so (1+tanA tanB)/(tanA- tanB) =(1+1)/-(sqrt23) =-2 sqrt 23
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