InterviewSolution
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InterviewSolution
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Number of solutions (s) of the equation `(sin x)/(cos 3x) +(sin 3x)/(cos 9x)+(sin 9x)/(cos 27 x)=0` in the interval `(0, pi/4)` is __________. |
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Answer» Correct Answer - 6 `(sin x)/(cos 3x)+(sin 3x)/(cos 9x)+(sin 9x)/(cos 27 x)=0` or `(2 sin x cos x)/(2 cos 3x cos x)+(2 sin 3x cos 3x)/(2 cos 9x cos 3x)+(2 sin 9x cos 9x)/(2 cos 27 x cos 9x)=0` or `(sin (3x-x))/(2 cos 3x cos x)+(sin (9x-3x))/(2 cos 9x cos 3x)+(sin (27x -9x))/(2 cos 27 x cos 9x)=0` or `(tan 3x-tan x)+(tan 9x-tan 3x)+(tan 27x-tan 9x)=0` or `tan 27 x-tan x=0` or `tan x=tan 27 x` `rArr 27x=n pi +x, n in I` or `x=(npi)/26, n in I`. or `x=pi/26, (2pi)/26, (3pi)/26, (4pi)/26, (5pi)/26, (6pi)/26` Hence, there are six solutions. |
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