A circular arc of radius ' 1 ' subtends an angle of ' x ' radians, 0

Question

A circular arc of radius ' 1 ' subtends an angle of ' $x$ ' radians, $0 < x < \frac{π}{2}$ as shown in the figure. The point ' $R$ ' is the point of intersection of the two tangent lines at P \& Q. Let T(x) be the area of triangle PQR and $S (x)$ be area of the shaded region. Then $Lim_{x \to 0} \frac{T ( x )}{S ( x )} =$

TestHub · Accepted Answer

T ( x ) = 2 1 ​ . PR . RQ sin ( π − x ) = 2 1 ​ ( tan 2 2 x ​ ) ⋅ sin x = tan 2 x ​ − 2 s i n x ​

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