Question

Angle between the curves $y=\sin x,y=\cos x$ is -

• A. $\frac{\pi }{4}$
• B. ${\tan }^{-1}\sqrt{2}$
• C. ${\tan }^{-1}2\sqrt{2}$
• D. None of these

Answer 1

The correct option is C ${\tan }^{-1}2\sqrt{2}$

$y=\sin x$ $y=\cos x$
$\Rightarrow m_1=\cos x$ $\Rightarrow m_2=-\sin x$
$\therefore y=\sin x;y=\cos x$
$\Rightarrow \sin x=\cos x$
$\Rightarrow \tan x=1$
$\Rightarrow x=\frac{\pi }{4};y=\frac{1}{\sqrt{2}}$
The point of intersection $(\frac{\pi }{4},\frac{1}{\sqrt{2}})$
$\Rightarrow m_1=\frac{1}{\sqrt{2}},m_2=-\frac{1}{\sqrt{2}}$
$\Rightarrow \tan \theta =\left(\frac{\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}}{1-\frac{1}{2}}\right)$
$\Rightarrow \theta ={\tan }^{-1}(\frac{2}{\sqrt{2}}\times \frac{2}{1})$
$\Rightarrow \theta ={\tan }^{-1}\left(2\sqrt{2}\right)$
Hence, option 'C' is correct.