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If tanA+sinA=m and m^(2)-n^(2)=4\sqrt(mn) then prove that tanA-sinA=n

If tanA+sinA=m
and m^(2)-n^(2)=4\sqrt(mn)
then prove that tanA-sinA=n

Grade:10

1 Answers

Vikas TU
14149 Points
6 years ago
Given as m=tan A+sinA 
and 
n= tanA-sinA 
now squaring them and subtratcing it is given also,
m2-n2= (tan A+sinA)2-( tanA-sinA)2 
=4tanA.SinA1 
mn= (tan A+sinA) (tanA-sinA) 
mn=tan2A-Sin2A 
mn= Sin2A(1/Cos2A-1) 
mn= Sin2A(1-Cos2A/Cos2A) 
mn= Sin2A(Sin2A/Cos2A) 
mn=Sin2A. tan2A 
sqrt(mn)=SinA.tanA2 
from 1, 
m2-n2=4tanA.SinA 
from 2, 
m2-n2=4sqrt(mn) 

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