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given cot A = 4/5
to prove (sin A + cos A)/(sin A - cosA) = 9
as cot A = 4/5 = cos A/sin A = 4/5 (1)
let us divided through by sin A
LHS =>
(sin A/sin A+cos A/sin A)/sin A/sin A - cos A/sin A)
=> (1 + 4/5)/(1-4/5) [ substituting cosA/sinA = ,4/5 from equation 1 ]
=> (9/5)/(1/5)
=> 9/5 * 5/1
=> 9 = RHS hence proved
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