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cos A sin A +1coĹ A + sin A1= cosec A + cot A, using the identity cosec Alt coa |
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Answer» (cos A- sin A + 1)/(cos A + sin A - 1). Divide both numerator and the denominator by sinA.the sum becomes (cot A - 1 + cosec A)/(cot A + 1 -cosec A) =(cosec A + cot A - 1)/(cotA - cosec A +1) ={cosecA+cotA-(cosec^2 A- cot^2 A)}/Dr where Dr=cotA-cosecA+1 ={(cosecA+cotA)-(cosecA+cotA)(cosecA-cotA)}/ Dr. =[(cosecA+cotA){1-(cosecA-cotA)}]/Dr ={(cosecA+cotA)(1-cosecA+cotA)}/Dr =(cosecA+cotA)(cotA-cosecA+1)/Dr =(cosecA+cotA).Dr/Dr =cosecA+cotA. |
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