If x cos θ + y sin θ = p is the normal form and y = m x + c is the slope - intercept form of the line x + 2 y + 1 = 0 , then tan - 1 tan θ + m + c =

Question

If x cos θ + y sin θ = p is the normal form and y = m x + c is the slope - intercept form of the line x + 2 y + 1 = 0 , then tan - 1 tan θ + m + c =, 0, π 2, π, π 4

MARKS App · Accepted Answer

x + 2 y + 1 = 0 ⇒ y = - 1 2 x - 1 2 is the slope intercept form so m = - 1 2 , C = - 1 2 ⇒ x 5 + y 5 / 2 = - 1 5 is the normal form so cos θ = 1 5 , sin θ = 2 5 , tan θ = 2 tan - 1 2 - 1 2 - 1 2 = tan - 1 1 = π 4

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