If sum of all the solutions of the equation $8 \cos x . (\cos (\frac{π}{6} + x) . \cos (\frac{π}{6} - x) - \frac{1}{2}) = 1$ in [0,π] is kπ, then k is equal to:

20/9

2/3

13/9

8/9

Solution

13/9

$8 \cos x . (\cos^{2} \frac{π}{6} - \sin^{2} x - \frac{1}{2}) = 1 \Rightarrow 8 \cos x (\frac{3}{4} - \frac{1}{2} - 1 + \cos^{2} x) = 1 \Rightarrow 8 \cos x (\frac{- 3 + 4 \cos^{2} x}{4}) = 1 \Rightarrow \cos 3 x = 1 \Rightarrow \cos 3 x = \frac{1}{2} \Rightarrow 3 x = \frac{π}{3}, \frac{5 π}{3}, \frac{7 π}{3} \Rightarrow x = \frac{π}{9}, \frac{5 π}{9}, \frac{7 π}{9} \Rightarrow s u m = \frac{13 π}{9} \Rightarrow k = \frac{13}{9}$

Some More Questions From Application of Integrals Chapter

A small firm manufactures necklaces and bracelets. The total number of necklaces and bracelets that it can handle per day is at most 24. It takes one hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16. If the profit on a necklace is ` 100 and that on a bracelet is ` 300. Formulate on L.P.P. for finding how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.

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Application Of Integrals

If sum of all the solutions of the equation $8 \cos x . (\cos (\frac{π}{6} + x) . \cos (\frac{π}{6} - x) - \frac{1}{2}) = 1$ in [0,π] is kπ, then k is equal to:

20/9

2/3

13/9

8/9

Some More Questions From Application of Integrals Chapter

Solve the following L.P.P. graphically :
Minimise Z = 5x + 10y
Subject to x + 2y ≤ 120
Constraints x + y ≥ 60
x – 2y ≥ 0
and x, y ≥ 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Application Of Integrals

If sum of all the solutions of the equation 8 cos x. cos π6+x.cosπ6-x-12 = 1 in [0,π] is kπ, then k is equal to: 20/9 2/3 13/9 8/9

Some More Questions From Application of Integrals Chapter

Solve the following L.P.P. graphically :Minimise Z = 5x + 10ySubject to x + 2y ≤ 120Constraints x + y ≥ 60 x – 2y ≥ 0and x, y ≥ 0

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If sum of all the solutions of the equation $8 \cos x . (\cos (\frac{π}{6} + x) . \cos (\frac{π}{6} - x) - \frac{1}{2}) = 1$ in [0,π] is kπ, then k is equal to:

20/9

2/3

13/9

8/9

Solve the following L.P.P. graphically :
Minimise Z = 5x + 10y
Subject to x + 2y ≤ 120
Constraints x + y ≥ 60
x – 2y ≥ 0
and x, y ≥ 0