Question

prove that cos theta minus sin theta + 1 upon cos theta + sin theta + 1 is equal to cos theta + cot theta​

Answer 1

Answer:

heya!!! here u go mate!!!

Given,

Radius = 21 cm  

θ = 60°

(i) Length of an arc = θ/360°×Circumference(2πr)

∴ Length of an arc AB = (60°/360°)×2×(22/7)×21

= (1/6)×2×(22/7)×21

Or Arc AB Length = 22cm

(ii) It is given that the angle subtend by the arc = 60°

So, area of the sector making an angle of 60° = (60°/360°)×π r2 cm2

= 441/6×22/7 cm^2

Or, the area of the sector formed by the arc APB is 231 cm^2

(iii) Area of segment APB = Area of sector OAPB – Area of ΔOAB

Since the two arms of the triangle are the radii of the circle and thus are equal, and one angle is 60°, ΔOAB is an equilateral triangle. So, its area will be √3/4×a^2 sq. Units.

Area of segment APB = 231-(√3/4)×(OA)^2

= 231-(√3/4)×21^2

Or, Area of segment APB = [231-(441×√3)/4] cm^2

Answer 2

Answer:

hope it will help you

Step-by-step explanation:

good night