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Question Number 133601 by help last updated on 23/Feb/21

Answered by benjo_mathlover last updated on 23/Feb/21

 ((sin^2  θ)/(sin θ−cos θ)) + ((cos^2 θ)/(cos θ−sin θ)) =   ((cos^2 θ−sin^2 θ)/(cos θ−sin θ)) = cos θ+sin θ

$$\:\frac{\mathrm{sin}^{\mathrm{2}} \:\theta}{\mathrm{sin}\:\theta−\mathrm{cos}\:\theta}\:+\:\frac{\mathrm{cos}\:^{\mathrm{2}} \theta}{\mathrm{cos}\:\theta−\mathrm{sin}\:\theta}\:= \\ $$$$\:\frac{\mathrm{cos}\:^{\mathrm{2}} \theta−\mathrm{sin}\:^{\mathrm{2}} \theta}{\mathrm{cos}\:\theta−\mathrm{sin}\:\theta}\:=\:\mathrm{cos}\:\theta+\mathrm{sin}\:\theta \\ $$

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