1+cos theta / sin theta = sin theta /1- cos theta
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LHS=
1+cosθ−sinθ
1+cosθ+sinθ
=
(1+cosθ−sinθ)(1+cosθ+sinθ)
(1+cosθ+sinθ)(1+cosθ+sinθ)
=
(1+cosθ)cosθ
1+cosθ+sinθ+cosθsinθ
=
(1+cosθ)cosθ
(1+sinθ)(1+cosθ)
=
cosθ
1+sinθ
=RHS
Hence proved
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