Prove that cos theta - sin theta +1/cos theta + sin theta - 1 =cosec theta + cot theta
Answers
Answered by
8
refer to the attachment ✌✌✌✌✌
Attachments:
Answered by
7
Answer:
LHS = (cos∅ - sin∅ + 1)/(cos∅ + sin∅-1)
dividing sin∅ both Numerator and denominator.
= (cos∅/sin∅ - sin∅/sin∅ + 1/sin∅)/(cos∅/sin∅ + sin∅/sin∅ - 1/sin∅)
= (cot∅ - 1 + cosec∅)/(cot∅ + 1 - cosec∅)
now, put 1 = cosec²∅ - cot²∅ in numerator
= {cot∅ + cosec∅ - (cosec²∅-cot²∅)}/(cot∅-cosec∅ +1)
= (cosec∅+cot∅)(1 - cosec∅ + cot∅)/(cot∅-cosec∅+1)
= cosec∅ + cot∅ = RHS
Step-by-step explanation:
Similar questions