the difference oftheirperimetersis60cosh-sindA+1- cosec A + cotA1cOSA-

1.	the difference oftheirperimetersis60cosh-sindA+1- cosec A + cotA1cOSA- sin328. Prove thatcosA + sinA-1ORWithout using tables, find the value of
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.

the difference oftheirperimetersis60cosh-sindA+1- cosec A + cotA1cOSA- sin328. Prove thatcosA + sinA-1ORWithout using tables, find the value of

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.