Question

show cos theta - sin theta + 1 divided by cos theta + sin theta -1 = cosec theta + cot theta

Answer 1

Answer:

Step-by-step explanation:

Ques- Cos⊙-sin⊙+1/cos⊙+sin⊙-1= cosec⊙+cot⊙

We will use the identity {cosec^2⊙ = 1-cot^2⊙}

Dividing the numerator and denominator by sin⊙ we get

Cot⊙-1+cosec⊙/cot⊙+1-cosec⊙

Multiplying numerator and denominator by cot theta +cosec theta we get

Cot theta -1 +codec theta *cot theta + cosec theta / cot theta + 1 - cosec theta *cot theta + cosec theta

After multiplying we get

(Cot theta - 1 + cosec theta)( cot theta + cosec theta ) / cot^2 theta+ cot theta.cosec theta + cot theta +cosec theta - cosec theta.cot theta - cosec^2 theta

Then you cancel cot theta.cosectheta with the -ve cot theta.cosectheta

Then you write ( -1) in place of ( cot^2theta- cosec^2 theta )

Then cancel the denominator with (cot theta -1 + cosectheta) in the numerator

We are the left with (cot theta + cosec theata ) which is the RHS

Hope this answer helps you and does not dissappoint you☺