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Can plz U help me solve this? If(tanA+sinA)=m and (tanA-sinA)=n, prove that, m 2 -n 2 =4sqrt(mn).

Can plz U help me solve this?
If(tanA+sinA)=m and
(tanA-sinA)=n, prove that,
m2-n2=4sqrt(mn).

Grade:10

1 Answers

Vikas TU
14149 Points
5 years ago
Taking L.H.S.
m^2 – n^2
=> (m +n) (m – n)
=> (2tanA) (2sinA)
=> 4tanAsinA …...............................(!)
 
Taking R.H.S
 
4sqrt.(mn)
4sqrt(tan^2A – sin^2A)
4sqrt(sin^2A/cos^2A –   sin^2A)
4sqrt(sin^2A(sec^2A – 1)
4sqrt(sin^2A*tan^2A)
4sqrt (sinA * tanA) …..................(2)
 
From the eqns. (1)  and (2)
 
L.H.S  =  R.H.S

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