Area under the curveHard

Question

For two curves C1 : y = 1 - cotx, x ∈ (0, π) and C2 : Y = 2|x| + λ to touch each other value of λ can be -

Options

A.
B.
C.
D.

Solution

C1 : y = 1 - cotx   x ∈ (0, π)
C2 : y = 2x + λ (for interval of C1)
for C1 and C2 to touch :
⇒ cosec2x = 2 ⇒ x =
for touch : 1 - cot + λ ⇒ λ =
and 1 - cot = 2. + λ ⇒ λ = 2 -

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