Question

The tangent to the curve $x=a\sqrt{\left(cos2\theta \right)}cos\theta ,y=a\sqrt{\left(cos2\theta \right)}sin\theta$ at the point corresponding to
​$\theta =\frac{\pi }{6}$ at

• A. parallel to the x-axis
• B. parallel to the y-axis
• C. parallel to line y = x
• D. none of these

Answer 1

The correct option is C parallel to line y = x

$f\left(x\right)=\frac{\pi }{2}$ (a constant function)
$\Rightarrow {\varphi }^{\prime }\left(x\right)=0$