Question

sin theta/1- cos theta = cosec theta + cot theta​

Answer 1

Answer

cosecA(1+cosA)(cosecA–cotA) = 1

On taking LHS

cosecA(1+cosA)(cosecA–cotA)

=> cosecA(1+cosA)(1/sinA–cosA/sinA)

=> cosecA(1+cosA)(1–cosA)/sinA

=> cosecA/sinA(1+cosA)(1–cosA)

=> 1/sin²A (1–cos²A)

{ Because cosecA = 1/sinA and a²–b²=(a+b)(a–b) }

=> sin²A/sin²A

=> 1 = R.H.S. { Because 1–cos²A = sin²A }

Answer 2

Answer:

(sin theta )(1+cos theta)/(1-cos theta)(1+costheta)

(sin theta +sin theta cos theta)/(1-cos²theta)

(sin theta+sin theta cos theta) /(sin²theta)

(sin theta/sin²theta)+(sin theta cos theta /sin²theta)

cosec theta cot theta

Step-by-step explanation:

rationalising denominator by (1+cos theta)then proceed as follows