InterviewSolution
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InterviewSolution
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The number of all the possible triplets `(a_1,a_2,a_3)`such that `a_1+a_2cos(2x)+a_2sin^2(x)=0`for all `x`is0 (b)1 (c) 3(d) infinite |
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Answer» Correct Answer - d Given, ` a_1 + a_2 cos 2x + a _3 sin ^(2) x = 0, AA x ` ` rArr a _1 + a_2 cos 2x + a _3 ((1 - cos 2x)/(2x)) = 0, AA x ` ` rArr (a_1 + (a_3)/(2)) + (a_2 - (a_3)/(2)) cos 2 x = 0, AA x ` ` rArr a_1 + (a_3)/(2) = 0 and a_2 - (a_3)/(2) = 0 ` ` rArr a _1 = - (k)/(2), a_2 = (k)/(2) , a_3 = k `, where `k in R` Hence, the solutions, are ` (-(k)/(2), (k )/(2), k)`, where k is any real number. Thus, the number of triplets is infinite. |
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