Question

Solve : sin 7x + sin 4x + sinx = o

Answer 1

=(sin7x+sinx) +sin4x
=sin(4x+3x) +sin(4x-3x) +sin4x
so by using: sin(A+B) +sin(A-B) =2sins. cosB
2sin4x.cos3x+sin4x
taking sin4x common
sin4x(2cos3x+1)=0
So, either sin4x=0. OR. 2cos3x+1=0
sin4x=sin0. cos3x= -1/2
so, 4x=nΠ cos3x=cosΠ\3
x=nΠ\4. OR. 3x=2mΠ±Π\3
so, x=2mΠ\3±Π\9
so, the possible values of x are
x=nΠ\4 OR x=2mΠ\3±Π\9

Answer 2

Answer:

Hope this helps you

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Thank You❤