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AP EAMCET · Maths · Differentiation

If \(f(t)=\frac{1+\operatorname{cosec} t}{1-\operatorname{cosec} t}\) for \(0 < t < \frac{\pi}{2}\) and \(f^{\prime}(t)=f(t) g(t)\), then \(g(t)=\)

  1. A \(-4 \operatorname{cosec} 2 t\)
  2. B \(4 \operatorname{cosec} 2 t\)
  3. C \(2 \sin 2 t\)
  4. D \(4 \operatorname{cosec} t\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(4 \operatorname{cosec} 2 t\)

Step-by-step Solution

Detailed explanation

Given, \(f(t)=\frac{1+\operatorname{cosec} t}{1-\operatorname{cosec} t}\) Differentiating w.r.t. \(t\), we get \((1-\operatorname{cosec} t)(-\operatorname{cosec} t \cot t)\)…