Question

if cosA/sinB=m and cosA/sinA=n then (m^2-n^2)sin^2A

Answer 1

L.H.S= (m2+n2)cos2b

= {(cosa/cosb)2 +(cosa/sinb)2}cos2b

= {(cos2a/cos2b) +(cos2a/sin2b)}cos2b

= (cos2a.sin2b +cos2a.cos2b / cos2b.sin2b)cos2b

= cos2a(sin2b+cos2b) / sin2b

= cos2a / sin2b

R.H.S= n2

=(cosa/sinb)2

= cos2a / sin2b

Therefore, L.H.S=R.H.S

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