The number of solutions of the equation `cos6x+tan^2x+cos6xtan^2x=1`in – InterviewSolution

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1.	The number of solutions of the equation `cos6x+tan^2x+cos6xtan^2x=1`in the interval `[0,2pi]`is4 (b) 5(c) 6 (d)7A. 4B. 5C. 6D. 7
Answer» Correct Answer - D `cos 6x=(1-tan^(2) x)/(1+tan^(2) x) = cos 2x` `rArr 2 sin 2x. Sin 4x =0` `rArr sin x. cos x. sin 4x=0` `rArr x=n pi, 4pi = m pi, m, n in Z` `rArr x=n pi, x=(mpi)/4, m, n in Z` `:. x=0, pi/4, (3pi)/4, pi, (5pi)/4, (7pi)/4, 2pi`

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