The function f(θ)=ddθ∫0θdx1−cosθcosx satisfies the differential eq | Filo
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The function f(θ)=ddθ∫0θdx1−cosθcosx satisfies the differential equation

  1. dfdθ+2f(θ)cotθ=0
  2. dfdθ−2f(θ)cotθ=0
  3. dfdθ+2f(θ)=0
  4. dfdθ−2f(θ)=0
Correct Answer: Option(a)
Solution: [a] we have f(θ)=ddθ∫0θdx1−cosθcosx =11−cos2θ=cosec2θ (using Leibnitz?s Rule) ⇒df(θ)dθ=−2cosec2θcotθ ⇒df(θ)dθ+2f(θ)cotθ=0
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