Grade 10Trigonometry
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
and m^(2)-n^(2)=4\sqrt(mn)
then prove that tanA-sinA=n
1 Answer
Vikas TU
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.SinA1
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.tanA2
from 1,
m2-n2=4tanA.SinA
from 2,
m2-n2=4sqrt(mn)
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