Home
Class 10
MATHS
Figure shows a sector of a circle with c...

Figure shows a sector of a circle with centre O and angle `'theta'`. Prove that:
(a) Perimeter of shaded region is `r(tan theta+sec theta+ (pi theta)/(180^@)-1) units`
(b) area of the shaded region is
`r^2/2 (tan theta-(pi theta)/(180^@))sq. units`

Text Solution

Verified by Experts

The correct Answer is:
`=r^2/2[ tan theta-(pi theta)/(180^@)]sq. units`
Promotional Banner

Topper's Solved these Questions

  • AREA RELATED TO CIRCLES

    ZEN PUBLICATION|Exercise TEXTUAL EXERCISES (EXERCISE 5.1)|5 Videos

  • AREA RELATED TO CIRCLES

    ZEN PUBLICATION|Exercise TEXTUAL EXERCISES (EXERCISE 5.2)|14 Videos

  • AN INTRODUCTION TO TRIGONOMETRY

    ZEN PUBLICATION|Exercise ZEN ADDITIONAL QUESTIONS ( HOTS (HIGHER ORDER THINKING SKILLS) - QUESTIONS) ( IIT/Olympiad/IMO)|10 Videos

  • ARITHMETIC PROGRESSIONS

    ZEN PUBLICATION|Exercise ZEN ADDITIONAL QUESTIONS (HOTS [HIGHER ORDER THINKING SKILLS] - QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

Show that cot theta +tan theta =sec theta cosec theta

Prove that (1+cot theta - cosec theta)(1+tan theta + sec theta) =2 .

Prove that (tan theta + sin theta)/(tan theta - sin theta) =(sec theta +1)/(sec theta-1)

( 1 + tan theta + sec theta ) ( 1 + cot theta - cosec theta ) =

Prove that the area of a segment of a circle with radius r and sector angle theta is r^2/2[(pi theta)/180^@-sin theta]

The general solution of tan 2 theta tan theta = 1 is theta =

Prove that: (sin theta - cos theta +1)/(sin theta + cos theta -1) = (1)/(sec theta - tan theta)

(tan theta)/(1-cot theta)+(cot theta)/(1-tan theta)=1+sec theta cosec theta

Prove that (sec theta + tan theta)^(2) = (cosec theta +1)/(cosec theta -1) .

If sec theta+tan theta=1.5 then tan theta=