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The number of solutions of the equation tan 3x = sin 6x in [ 0, Π/6) U ( Π/6,Π/2] is

The number of solutions of the equation tan 3x = sin 6x in [ 0, Π/6) U ( Π/6,Π/2] is

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
tan3x = sin 6x => tan3x = 2sin3xcos3x => sin3x/cos3x = 2sin3xcos3x.
Hence one solution is x = 0.
2cos23x = 1 => cos23x = 1/2 => cos3x = 1/√2 => x = cos-1(1/√2)/3 =  π/12.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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