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prove that cos theta minus sin theta + 1 / cos theta + sin theta minus 1 is equal to cosec theta + cot theta

prove that cos theta minus sin theta + 1 / cos theta + sin theta minus 1 is equal to cosec theta + cot theta

Grade:10

1 Answers

Arun
25763 Points
3 years ago
Dear student
 

take Lhs

cosA-sinA+1 /cos A + sinA-1

numerator and denominator dividng by sinA

cosecA + CotA - 1 / cotA - CosecA + 1

 

cosecA + CotA - ( cosecA^2 - CotA^2) / cotA - CosecA + 1

 

cosecA + CotA - (cosecA + CotA) (cosecA - CotA) /cotA - CosecA + 1

 

(cosecA + CotA)( cotA - CosecA + 1 ) / cotA - cosecA +1

 

cosecA + CotA

 

Regards

Arun (askIITians forum expert)

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