Question

Plz answer this question. .............. WITH FULL SOLUTION. ...NO SHORTCUTS....AND NO GUESSING.

$ar \: of \: shaded \: region = \frac{ {r}^{2} }{2} \times ( \tan(theta) - \frac{\pi \times theta}{180})$

Answer 1

    Area of the shaded region ABC is simply the area of the triangle OABC minus the area of circular sector OAC.  ΔOAB seems to be a right angle triangle, with ∠A = 90°.  AB seems to be the tangent.

  OA = radius = r. 

    AB/OA = Tan θ°
So  AB = OA Tanθ° = r Tan θ°.

ar(ΔOAB) = 1/2 * OA * AB
                = 1/2 * r² * Tan θ°

ar(Sector OAB) = π r² * (θ°/360°) ,         as θ is in degrees.
                = 1/2 * r² θ° * (π/180°) 

Shaded region = 1/2 * r² * [Tanθ° - π θ°/180°]

Answer 2

This is ur answer hope it will help u