Question

$A$ssertion $A$: The angle between the curves $y=$ sinx, $y=$ cosx is $\tan \sqrt{2}$.
Reason (R) The slopes of their tangents at $(\frac{\pi }{4},\frac{1}{\sqrt{2}})$ are $\frac{1}{\sqrt{2}}$ and $-\frac{1}{\sqrt{2}}$ respectively.

• A. Both A and R are true R is the correct explanation
  of A
• B. Both A and R are true but R is not correct
  explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

Answer: (D)

A is false but R is true

$\frac{dy}{dx}=cosx=m_1$
$\frac{dy}{dx}=-sinx=m_2$
$tan\theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|$
$=\frac{cosx+sinx}{1-sinxcosx}$
$\frac{\frac{1}{\sqrt{2}+\frac{1}{\sqrt{2}}}}{1-\frac{1}{2}}$
$=3\sqrt{2}$
$m_1=\frac{1}{\sqrt{2}}$
$m_2=-\frac{1}{\sqrt{2}}$