Question

If tan θ + sin θ = m and tan θ - sin θ = n then (m^2-n^2)^2 = 16mn

Answer 1

Answer:

tan θ + sin θ) = m and (tan θ − sin θ) = n..

L.H.S = R.H.S

Step-by-step explanation:

To Prove: (m2 − n2)2 = 16mn L.H.S. = (m2 − n2)2 = [(tan θ + sin θ)2 – (tan θ − sin θ)2]2 = (4tan θ sin θ)2 = 16 tan2 θ sin2 θ …(1) R.H.S. = 16mn = 16(tan θ + sin θ)(tan θ − sin θ) = 16(tan2 θ − sin2 θ) = 16 [{sin2 θ (1-cos2 θ)/cos2θ] = 16 x sin2 θ/cos2θ x (1-cos2 θ) = 16 tan2 θ sin2 θ …(2) From (1) and (2) L.H.S. = R.H.S.

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