Question

if cosA+sinA/cosA-sinA= 1+root of 3/1-root of 3, tell the value of A

Answer 1

by one of the law of properties
a/b= c/d then a+b/a-b=c+d/c-d
so, (cosA+sinA+cosA-sinA)/(cosA+sinA-cosA+sinA)=(1+root3+1-root3)/(1+root3-1+root3)
or 2cosA/2sinA=2/2root3
or cot A=cot 60
or A=60 degree

Answer 2

hello users ..........

given that :-

(cosA+sinA)/(cosA-sinA) = (1 +√3) / (1- √3)

we have to find 
A = ? 

solution :-
here ,
(cosA+sinA)/(cosA-sinA)

= cos A ( 1 + tan A) / cos A ( 1 - tan A) 

= (1 + tan A ) / ( 1- tan A ) 

now ,
(1 +√3) / (1- √3) 

= (1 + tan 60° ) / ( 1- tan 60° )       
because tan 60° = √3


now,
 by comparing
 (1 + tan A ) / ( 1- tan A ) and (1 + tan 60° ) / ( 1- tan 60° ) 

=> tan A = tan 60°

=> A = 60° answer 

(::) hope it helps (::)