InterviewSolution
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InterviewSolution
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The number of solutions of the equation `sin^3xcosx+sin^2xcos^2x+sinxcos^3x=1`in the interval `[0,2pi]`is/are0 (b) 2(c) 3 (d)infinite |
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Answer» Correct Answer - A `sin^(2) x cos x+sin^(2) x cos^(2) x+ sin x cos^(3)x=1` or `sin x cos x (sin^(2) x+sin x cos x + cos^(2)x)=1` or `(sin 2x)/2 (1+(sin 2x)/2)=1` or `sin 2x(2+sin 2x)=4` or `sin^(2) 2x+2 sin 2x-4 =0` or `sin 2x=(-2 pm sqrt(4+16))/2=-1 pm sqrt(5)` This is not possible since `-1 le sin 2x le 1`. Hence, the given equation has no solution. |
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