Question

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

Answer 1

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

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Answer 2

Step1, Divide the whole numerator and denominator of the LHS by sin theta.

Step2, Multiply both numerator and denominator by the numerator.

Step3, Rearrange and get the RHS

Hope it helps...