Number of solution(s) of the equation cos(2x+π3)=1 in [0,3π] is/are
A
3.00
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B
03
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C
3
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D
3.0
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Solution
Number of solutions of the equation cos(2x+π3)=1 in [0,3π] are same as the points of intersection of the graphs y=cos(2x+π3) and y=1.
In y=cos(2x+π3) fundamental function involved is cosx , whose graph is given by
Apply the stretch transformation by 2 units in y=cosx to get y=cos2x as shown below Now apply the horizontal shift by π6 to get y=cos(2x+π3) as shown below Now let us calculate the number of point of intersections of y=1 and y=cos(2x+π3) in [0,3π] from the graph Clearly in [0,3π] , there are 3 points of intersection.
Hence given equation have 3 solutions.