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What is the general solution of the equation cosx +3sinx +sin3x -cos3x=0 ?

What is the general solution of the equation   cosx +3sinx +sin3x -cos3x=0 ?

Grade:11

1 Answers

Aditya Gupta
2081 Points
5 years ago
Simply substitute sin3x=3s-4s^3, s being sinx and cos3x= 4c^3-3c, c being cosx. Then use the identity c^3+s^3= (c+s)(1-sc) and simplify. You will then get two conditions- either sinx=0 or -1= 2sc+2c^2
But the latter is not possible since the LHS in it is equal to sin2x+cos2x+1 whose minimum value is greater than -1. Hence sinx= 0 or x= nπ is the complete solution

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