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Question

cot4θtan4θ=?


  1. 2sec2θsec4θ2cosec2θ+cosec4θ

  2. 2sec2θsec4θ

  3. 2cosec2θ+cosec4θ

  4. none of the above


Solution

The correct option is A

2sec2θsec4θ2cosec2θ+cosec4θ


cot4θtan4θ=(cot2θ)2(tan2θ)2=(cosec2θ1)2(sec2θ1)2=cosec4θ+12cosec2θ(sec4θ+12sec2θ)=cosec4θ+12cosec2θsec4θ1+2sec2θ=2sec2θsec4θ2cosec2θ+cosec4θ

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