Here, 2sinθ−sin2θ2sinθ+sin2θ=2sinθ−2sinθcosθ2sinθ+2sinθcosθ [∵sin2θ=2sinθcosθ]
=2sinθ(1−cosθ)2sinθ(1+cosθ)
=1−cosθ1+cosθ
=2sin2θ/22cos2θ/2 ∵[cos2θ=1−2sin2θcos2θ=2−cos2θ−1]
=tan2θ/2
=1−2tanθ/2tanθ ⎡⎢
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⎢⎣tan2θ=2tanθ1−tan2θ⇒1−tan2θ=2tanθtan2θ⇒tan2θ=1−2tanθtan2θ⎤⎥
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⎥⎦.