If tan A - sin2 Ac= cos 2 A, then show that sin2 A =1/2
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tanA-sin2A=(sinA/cos A)-2sinA.cosA
=sinA{(1/cosA)-2cosA}
=sinA{1-2cos^2A}
=sinA{sin^2A+cos^2A-2cos^2A}
=sinA(sin^2A-cos^2A)
=-sinA. cos2A=cos2A given
cos2A (1+sinA)=0
cos2A=0=cos90
2A=90, A=45
sin2A=sin 90=1
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