sin6x+3sin4x.cos2x=0 find solution set sin6x+3/2(sin6x+sin2x)=0 5sin6x+3sin2x=0 I got stuck here.
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Originally Posted by kastamonu sin6x+3sin4x.cos2x=0 find solution set sin6x+3/2(sin6x+sin2x)=0 5sin6x+3sin2x=0 I got stuck here. Is it or ? -Dan
write sin 6x = sin( 4x + 2x) = ......
sin2x
Originally Posted by Idea write sin 6x = sin( 4x + 2x) = ...... I couldn't get anything.
Let y = 2x so we have 5.sin(3y) + 3.sin(y) = 0 where sin(3y) = sin(2y+y) = sin(2y).cos(y) + cos(2y).sin(y) = 2.sin(y).cos^2(y) + sin(y).(1-2.sin^2(y)) = 2.sin(y)(1-sin^2(y)) + sin(y) - 2.sin^3(y) = 3.sin(y) - 4.sin^3(y)
Plug that in for sin(3y). Then, let . You wind up with a cubic equation in . Solve for (you have something for the form , so implies or ). Once you solve for , you have , so take arcsin of both sides. Then, you have .
you could also linearize the equation giving two sets of solutions
Thanks.
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