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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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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
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