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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Trigonometric Equations

NDA 2016 · Mathematics · Trigonometric Equations

Consider the equation: k x+ 2 x=2 k-7 If the equation possesses...

Consider the equation: ksin⁡x+cos⁡2x=2k−7k \sin x+\cos 2 x=2 k-7 If the equation possesses solution, then what is the maximum value of k ?

Options

  1. A1
  2. B2
  3. C4
  4. D6

Correct answer

D. 6

Step-by-step solution

For maximum value of KK, sin⁡x=1\sin x=1K±K2−16K+644=1⇒(±)K2−16K+64=(−K+4)\begin{aligned} & \frac{K \pm \sqrt{K^2-16 K+64}}{4}=1 \\ & \Rightarrow( \pm) \sqrt{K^2-16 K+64}=(-K+4) \end{aligned}Squaringbothsides,wegetSquaring both sides, we get\begin{aligned} & K^2-16 K+64=K^2+16-8 K \\ & \Rightarrow 8 K=48 \\ & \Rightarrow K=6 \end{aligned}$$
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