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#1 2007-11-02 00:29:49

tony123
Member
Registered: 2007-08-03
Posts: 228

acute angles a and b

Find the acute angles a and b that satisfy the following simultaneous equations:

2sin 2b =3 sin 2a

tan b =3 tan a

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#2 2007-11-12 01:45:47

gyanshrestha
Member
Registered: 2007-11-06
Posts: 41

Re: acute angles a and b

let  2sin2b = 3sin2a  -----------  (I)
tanb  = 3tana ---------------II
from (I)
4sinb.cosb=6sina.cosa
multiplying both side by  II
we get
4sin^2 b =18 sin^2  a
4tan^2 b/(sq.root(1+tan^2 b)  =  18tan^2 a/(sq.root(1+tan^2 a)
now

36tan^2 a/sq.root(1+9tan^2 a) = 18tan^2 a/(sq.root(1+tan^2 a)
putting tan^a = x
we get
36x/sq.root(1+9x) = 18x/sq.root(1+x)
solving this equation we get
3 = 5x
which give tan^2 a =3/5



tan a =sq.root(3/5)
tan b =3.sq.root(3/5)


solved !!!!
yes
if there is mistake soryy in advanced


http://gyan.talkacademy.com.np

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