Question

solve proove 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)


Hence proved.....

Answer 2

Hola mate♡

Answer:-

Given that:-

1/ cosec theta + cot theta - 1 /Sin theta

Now..

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

cosec theta - cot theta / 1 -1 / Sin theta

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

1- 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)


Hence proved.♥