Question

Equation of a tangent to the curve $y\cot x=y^3\tan x$ at the point where the abscissa is $\frac{\pi }{4}$ is :

• A. $4x+2y=\pi +2$
• B. $4x-2y=\pi +2$
• C. $x=0$
• D. $y=0$

Answer 1

Answer: (A), (B), (D)

$y{\cot }^{2}x-y^3=0\Rightarrow y\left(y^2-{\cot }^{2}x\right)=0$
hence the curve is $y=0$ or $y^2={\cot }^{2}x$