Question

Prove that

1/cosec theta-cot theta - 1/sin theta = 1/sin theta - 1/cosec theta+cot theta ?????????

Answer 1

We have Given that

✨ 1/cosec theta + cot theta - 1/sin theta

        By proceeding.....

⭐1/cosec theta + cot theta × cosec theta - cot theta/cosec theta - cot theta - 1/sin theta

⭐cosec theta - cot theta/cosec² theta - cot² theta - 1/sin theta

⭐cosec theta - cot theta/1 - 1/sin theta

⭐sin theta(cosec theta - cot theta)-1/sin theta

➡1-cos theta - 1/sin theta

➡1/sin theta - cos theta/sin theta  - 1/sin theta

➡1/sin theta - cot theta - cosec theta 

➡1/sin theta - (cosec theta + cot theta)

➡1/sin theta - (cosec theta + cot theta)  × (cosec theta - cot theta)/cosec theta - cot theta)

➡ 1/sin theta - 1/(cosec theta - cot theta)

Answer 2

hope it will be helpful for you