AP EAMCET · Maths · Application of Derivatives
The angle between the curves \(y=\sin x\) and \(y=\cos x\) is
- A \(\tan ^{-1}(2 \sqrt{2})\)
- B \(\tan ^{-1}(3 \sqrt{2})\)
- C \(\tan ^{-1}(3 \sqrt{3})\)
- D \(\tan ^{-1}(5 \sqrt{2})\)
Answer & Solution
Correct Answer
(A) \(\tan ^{-1}(2 \sqrt{2})\)
Step-by-step Solution
Detailed explanation
Given that, \(y=\sin x\) ...(i) and \(y=\cos x\) ...(ii) From Eqs. (i) and (ii), \(\sin x=\cos x \Rightarrow \tan x=1 \Rightarrow x=\frac{\pi}{4}\) Slope \(\quad m_1=\frac{d y}{d x}=\cos x\) \(m_2=\frac{d y}{d x}=-\sin x\)…
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