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  • Can someone explain - If and y = 3sect, then the value of at,is : - Differential equations - JEE Main

If x= 3tant and y = 3sect, then the value of \frac{d^2 y}{d x^2} at t=\pi /4,is :

  • Option 1)

    3/2\sqrt{2}

  • Option 2)

    1/6\sqrt2

  • Option 3)

     

    1/3\sqrt{2}

  • Option 4)

     

    1/6

Answers (1)

best_answer

 

Second Order Differential Equation -

\frac{d^{2}y}{dx^{2}}= f\left ( x \right )

- wherein

\frac{d^{2}y}{dx^{2}}= \sin x

\\x = 3\tan(t) \Rightarrow \frac{dx}{dt} = 3\sec^2(t)\\ y = 3\sec (t) \Rightarrow \frac{dy}{dt} = 3\sec(t)\tan(t)

\\\frac{dy}{dx} = \frac{\tan(t)}{\sec(t)} = \sin(t)\\ \frac{d^2y}{dx^2} = \cos(t)\frac{dt}{dx} =\frac{\cos(t)}{3\sec^2(t)} = \frac{\cos^3(t)}{3} = \frac{1}{6\sqrt2}\;\;\; \left (at\;t=\frac{\pi}{4}\right )

 


Option 1)

3/2\sqrt{2}

Option 2)

1/6\sqrt2

Option 3)

 

1/3\sqrt{2}

Option 4)

 

1/6

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