If cot θ+cosec θ=2 cot θ, show that cot θcosec θ=2 cosec θ


Answer:


Step by Step Explanation:
  1. We have cot θ+cosec θ=2 cot θ By squaring both the sides, we get (cot θ+cosec θ)2=(2 cot θ)2cot2 θ+cosec2 θ+2 cot θ cosec θ=2 cot2 θcosec2 θ=2 cot2 θcot2 θ2 cot θ cosec θcosec2 θ+cosec2 θ=cot2 θ2 cot θ cosec θ+cosec2 θ  [ Adding cosec2 θ on both the sides. ]2 cosec2 θ=(cot θcosec θ)2cot θcosec θ=2 cosec θ
  2. Hence, cot θcosec θ=2 cosec θ.

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