InterviewSolution
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InterviewSolution
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Find the general solution for each of the following equation: `sin x + sin 3x + sin 5x = 0` |
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Answer» We have, `sin x+sin 3x+sinn 5x=0` `therefore (sin x+sin 5x) +sin 3x=0` `therefore 2 sin ((x+5x)/(2))cos ((5x-x)/(2))+sin3x=0` `therefore2 sin 3x cos 2x+sin 3x=0` `therefore sin3x(2 cos2x+1) =0` Either `sin 3x=0 or 2 cos 2x+1=0` i.e., `sin 3x=0 or cos 2x=-1/2` Now, `cos 2x=-cos ""(pi)/(2)` `cos 2x=cos(pi-(pi)/(3))` `cos 2x=cos ""(2pi)/(3)` `therefore sin 3x=0or cos 2x=cos ""(2pi)/(3)` `3pi=npi, n ne Zor 2x=2mpipm(2pi)/(3)` where` m inZ` Hence, `x=(npi)/(3)or x=mpipm (pi)/(3), wheren, m in Z` |
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