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if x belongs to [0,90],the number of solutions of the equation sin7x+sin4x+sinx=0 is

if x belongs to [0,90],the number of solutions
of the equation sin7x+sin4x+sinx=0 is

Grade:11

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
4 years ago
sin7x + sin4x + sinx = sin4x + 2sin4xcos3x = sin4x(2cos3x + 1) = 0
hence sin4x = 0 and cos3x = -1/2
x = nPI/2 and x = 2nPI ± 2PI/3
Now find how many are in 0 to 90

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