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Question

The angle of intersection of the curves y=2sin2 x and y= cos 2x at x =π6 is


A

π4

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B

π3

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C

π2

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D

2π3

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Solution

The correct option is D

2π3


We have,
y=sin2x...(1)y=cos 2x...(2) And
On differentiating equation (1) w.r.t x, we get
dydx=4 sin x cos x[dydx]xπ6=4(12)32=3=m1(say)
On differentiating equation (2) w.r.t x, we get
dydx=2 sin 2x[dydx]xπ6=2 sin π3=3=m2(say)
Hence, angle between the two curves is
θ=±tan1(m1m21+m1 m2)=±tan13=π3or2π3
Hence (b) is the correct answer.


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