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Question

sin2x1+cos2x=tanx

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Solution

sin2x1+cos2x=tanx
Taking L.H.S.
sin2x1+cos2x
Using trigonometric identity:
sin2x=2sinxcosx
cos2x=2cos2x11+cos2x=2cos2x
Therefore,
sin2x1+cos2x
=2sinxcosx2cos2x
=sinxcosx
=tanx
=R.H.S.
Hence proved that sin2x1+cos2x=tanx.

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