If cosec θ+cot θ=m, show that m21m2+1=cos θ.


Answer:

cos θ

Step by Step Explanation:
  1. It is given that cosec θ+cot θ=m.  (m21)=(cosec θ+cot θ)21=cosec2 θ+cot2 θ+2cosec θ cot θ1=(cosec2 θ1)+cot2 θ+2cosec θ cot θ=2cot2 θ+2cosec θ cot θ[cosec2 θ1=cot2 θ]=2cot θ (cot θ+cosec θ)
  2. Similarly, (m2+1)=(cosec θ+cot θ)2+1=cosec2 θ+cot2 θ+2cosec θ cot θ+1=(cot2 θ+1)+cosec2 θ+2cosec θ cot θ=2cosec2 θ+2cosec θ cot θ[1+cot2 θ=cosec2 θ]=2cosec θ (cosec θ+cot θ)
  3. From step 1 and step 2, we get m21m2+1=cot θcosec θ=cos θsin θ1sin θ=cos θ
  4. Thus, the value of m21m2+1 is cos θ.

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