InterviewSolution
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InterviewSolution
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The real roots of the equation `cos^7x+sin^4x=1`in the interval `(-pi,pi)`are __________, ________, and ________ |
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Answer» Correct Answer - `x= 0, pm pi/2` `cos^(7) x=1-sin^(4) x= (1-sin^(4) x)(1+sin^(2) x)` or `cos^(7) x = cos^(2) x(2-cos^(2) x)` or `cos^(2) x(cos^(5)x+cos^(2) x-2)=0` or `cos x =0` `rArr x=pm pi//2` in the given interval or `cos^(5) x+cos^(2)x-2=0`, which holds when `cos x=1`, hence `x=0`. Thus, there are total three solutions : `0, pm pi//2`. |
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