Question

In Figure, is shown a sector OAP of a circle with centre O, containing ∠θ. AB is a perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r [tan θ + sec θ + πθ/180° – 1]

Assertion (A): The value of each trigonometric ratio of an angle does not vary with the lengths of the sides of the triangle if the angle remains the same. Reason (R): In a right-angled triangle ABC, sin θ = BC/AC < 1 and cos θ = AB/AC < 1 as the hypotenuse is the longest side.