Question

To prove
CosA/1-tan A +sin A/1-cot A =sin A+cosA

Answer 1

 LS = (cosA)/(1-tanA)+(sinA)/(1-cotA) 

change tanA to sinA/cosA, cotA to cosA/sinA 
= (cosA)/(1-(sinA/cosA))+(sinA)/(1-(cosA/s... 

multiply the first term by cosA/cosA, 2nd term by sinA/sinA (really multiplying both terms by 1 
= ((cosa)(cosA))/(cosA-sinA)+((sinA)(sinA)... 

multiply the first term by -1/-1 to get a common denominator 
= -((cosA)(cosA))/(sinA-cosA)+((sinA)(sinx... 

add the fractions 
= (sin^2A-cos^2A)/(sinA-cosA) 

use difference of squares to factor the numerator 
= ((sinA+cosA)(sinA-cosA))/(sinA-cosA) 

sinA-cosA in the numerator cancels with sinA-cosA in the denominator 
=sinA+cosA

Answer 2

check this working. tan A= sinA/cosA