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Question

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

(a) π/4
(b) π/2
(c) π/3
(d) none of these

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Solution

(c) π/3

Given:x=π6Now,y=2sin2xdydx=4sinx cosxdydx=2 sin 2xm1=dydxx=π6=2×32=3Also,y=cos 2xdydx=-2 sin2xm2=dydxx=π6=-2 ×32=-3tan θ=m1-m21+m1m2=3+31-33=23-2=3θ=tan-13=π3

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