Question

If tan + sin =m and tan - sin =n show that m2 - n2 = 4 rootofmn

Answer 1

m2=(tan+sin)2
n2= (tan-sin)2

(tan+sin)2 = tan2+sin2+2 tan.sin
(tan+sin)2= tan2+sin2-2 tan.sin

L.H.S
tan2×sin2 + 2tan.sin-tan2-sin2=4tan.sin
R.H.S
4(root)tan2-sin2
4 (root)sin2/cos2-sin2
4(root)sin2-sin2.cos2/cos2
4(root)sin2(1-cos2)/cos2
4((root)tan2.sin2
4tan.sin=L.H.S