For the curve y = 3sin θcosθ,x=eθsinθ,0≤θ≤π; tangent is parallel to x-axis, then θ =
A
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B
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C
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Solution
The correct option is B Given y = 3 sin θcosθ, x = eθsinθ For tangent parallel to x-axis, we should have dydx = 0 ⇒dydx = 0 and dxdθ≠0 and ddθ(3sin2θ2) = 0 ⇒3cos2θ=0⇒2θ=π2 ⇒θ=π4 Note that for θ=π4,dxdθ=eθ[sinθ+cosθ]≠0.