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Question

The angle of intersection of curves. y = [|sin x| + |cos x|] and x2+y2=5 where [.] denotes greatest integral function is


A

π4

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B

tan1(12)

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C

tan1(2)

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D

none of these

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Solution

The correct option is C

tan1(2)


We know that. 1|sin x|+|cos x|2
y=[|sin x|+|cos x|]=1
Let P and Q be the points of intersection of given curves.
Clearly, the given curves meet at points where y = 1 so, we get
x2+1=5x=±2

Now, P(2, 1) and Q(-2, 1)
Differentiating x2+y2=5 w.r.t. x, we get 2x +
2ydydx=0dydx=xy(dydx)(2.1)=2 and (dydx)(2.1)=2
Clearly the slope of line y = 1 is zero and the slope of the tangents at P and Q are (-2) and (2) respectively.
Thus, the angle of intersection is tan1(2)
Hence the correct option is c


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