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Question

# Number of solutions of the equation tan2x=2cos(x+π) in (−π,π) is/are

A
4
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B
4.0
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C
04
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D
4.00
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Solution

## Number of solutions of the equation tan2x=2cos(x+π) in (−π,π) are same as number of points of intersection of y=tan2x and y=2cos(x+π) in (−π,π). Here fundamental functions involved are tanx and cosx. Whose graphs are given by and Now apply the stretch transformation by 2 units to y=tanx to get the graph of y=tan2x as shown below Now we will make transformation to the graph of y=cosx. First, apply the horizontal shift by π units to get y=cos(x−π) as shown below Further, apply stretch transformation along y by 2 units to get y=2cos(x+π) as shown below Now we will calculate the number of points of intersection in combined graph of y=tan2x and y=2cos(x+π) From the above graph, we can see there are 4 points of intersection in (−π,π). Hence the given equation have 4 solutions in (−π,π)

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