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TS EAMCET · Maths · Application of Derivatives

If the equation of a tangent drawn to the curve \(y=\cos (x+y),-1 \leq x \leq 1+\pi\) is \(x+2 y=k\), then \(k=\)

  1. A \(1\)
  2. B \(\frac{\pi}{4}\)
  3. C \(\frac{\pi}{2}\)
  4. D \(2\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{\pi}{2}\)

Step-by-step Solution

Detailed explanation

\begin{array}{rl} & y=\cos (x+y) ;-1 \leq x \leq 1+\pi \\ \Rightarrow & \frac{d y}{d x}=-\{\sin (x+y)\} \cdot\left(1+\frac{d y}{d x}\right) \\ \Rightarrow & \frac{d y}{d x}(1+\sin (x+y))=-\sin (x+y) \\ \Rightarrow & \frac{d y}{d x}=\frac{-\sin (x+y)}{1+\sin (x+y)} \\ \Rightarrow…