Question

The value of $x$ for which the tangents to the curves $y=x\cos x,y=\frac{\left(\sin x\right)}{x}$ are parallel to the axis of $x$ are roots of

• A. $\sin x=x,\tan x=x$
• B. $\cot x=x,\sec x=x$
• C. $\cot x=x,\tan x=x$
• D. $\tan x=x,\cot x=x$

Answer 1

The correct option is C $\cot x=x,\tan x=x$

1. $y=xcosx$

$\frac{dy}{dx}=-xsinx+cosx$

Since the tangent has to be parallel to x axis, slope would be zero.

$\Rightarrow x=cotx$

2. $y=\frac{sinx}{x}$

$\frac{dy}{dx}=\frac{xcosx-sinx}{x^2}$

Again, equating this to zero, we get $x=tanx$

Hence, option C is correct.