1-609 1-tanbB e . aB

1.	1-609 1-tanbB e . aB
Answer» (Tan A/1-Cot A) +( Cot A / 1 - Tan A )= Sec A.Cosec A + 1 LHS = (sin A/cos A) / [1- (cos A/sin A)] + (cos A/sin A) / [1- (sin A/cos A)] = (sin A/cos A) / [(sin A - cos A)/sin A] + (cos A/sin A) / [(cos A - sin A) /cos A] = (cos^2 A) / [sin A(cos A - sin A)] - (sin^2 A) / [cos A(cos A - sin A)] = (cos^3 A - sin^3 A) / [(cos A * sin A) (cos A - sin A)] = (1/cos A * sin A) (sin^2 A + cos^2 A + sin A cos A) = (1/cos A * sin A) (1+ sin A cos A) = [1 / (cos A sin A) + (cos A sin A) / (cos A sin A)] = sec A * csc A + 1 = RHS it's really hard for me to understand

Answer»

(Tan A/1-Cot A) +( Cot A / 1 - Tan A )= Sec A.Cosec A + 1

LHS = (sin A/cos A) / [1- (cos A/sin A)] + (cos A/sin A) / [1- (sin A/cos A)]

= (sin A/cos A) / [(sin A - cos A)/sin A] + (cos A/sin A) / [(cos A - sin A) /cos A]

= (cos^2 A) / [sin A(cos A - sin A)] - (sin^2 A) / [cos A(cos A - sin A)]

= (cos^3 A - sin^3 A) / [(cos A * sin A) (cos A - sin A)]

= (1/cos A * sin A) (sin^2 A + cos^2 A + sin A cos A)

= (1/cos A * sin A) (1+ sin A cos A)

= [1 / (cos A sin A) + (cos A sin A) / (cos A sin A)]

= sec A * csc A + 1 = RHS

it's really hard for me to understand

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