CATGeometry > Hard2cosθ\sqrt{2} \cos \theta2cosθ1(sinθ+cosθ)2\frac{(\sin \theta + \cos \theta)}{\sqrt{2}}2(sinθ+cosθ)2sinθ\sqrt{2} \sin \theta2sinθ✅ Correct Option: 4Related questions:CAT 2023 Slot 2A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a:ba: ba:b. If the radius of the circle is rrr, then the area of the triangle isCAT 2020 Slot 2The sum of the perimeters of an equlateral triangle and a rectangle is 90 cm90 \mathrm{~cm}90 cm the area, TTT , of the triangle and the area, RRR , of the rectangle, both in sq cm, satisfy the relationship R=T2R=T^{2}R=T2. If the sides of the rectangle are in the ratio 1:31: 31:3, then the length, in cm , of the longer side of the rectangle, isCAT 2023 Slot 1In a right-angled triangle △ABC\triangle A B C△ABC, the altitude ABA BAB is 5 cm5 \mathrm{~cm}5 cm, and the base BCB CBC is 12 cm12 \mathrm{~cm}12 cm. PPP and QQQ are two points on BCB CBC such that the areas of △ABP,△ABQ\triangle \mathrm{ABP}, \triangle \mathrm{ABQ}△ABP,△ABQ and △ABC\triangle \mathrm{ABC}△ABC are in arithmetic progression. If the area of △ABC\triangle \mathrm{ABC}△ABC is 1.51.51.5 times the area of △ABP\triangle \mathrm{ABP}△ABP, the length of PQ in cm , is