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Step-by-step explanation:
Given,
tan θ + sin θ = m
tan θ – sin θ = n
m2 – n2 = (tan2θ + sin2θ + 2 tan θ sin θ) – (tan2θ + sin2θ – 2 tan θ sin θ)
= 4 tan θ sin θ….(i)
mn = (tan θ + sin θ)(tan θ – sin θ)
= tan2θ – sin2θ
= (sin2θ/cos2θ) – sin2θ
= sin2θ(sec2θ – 1)
mn = sin2θ tan2θ
Taking square root on both sides,
√mn = sin θ tan θ….(ii)
From (i) and (ii),
m2 – n2 = 4√mn
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