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 \(k=\)
- A \(1\)
- B \(\frac{\pi}{4}\)
- C \(\frac{\pi}{2}\)
- D \(2\)
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…
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