Question

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 1

Answer: (A)

If $\sin x=\cos x\Rightarrow x=\frac{\pi }{4}$
$y=\sin x\Rightarrow {\left(\frac{dy}{dx}\right)}_{x=\pi /4}=\frac{1}{\sqrt{2}}$
If $y=\cos x\Rightarrow {\left(\frac{dy}{dx}\right)}_{x=\pi /4}=-\frac{1}{\sqrt{2}}$
$\tan \theta =\frac{m_1-m_2}{1+m_1{m}_2}=2\sqrt{2}\Rightarrow \theta ={\tan }^{-1}(2\sqrt{2})$