QJEEM19Ma95ff: JEE Main 2019 Mathematics - Class 12 JEEM19Ma95ff Solution: If   x 3 tan t and y 3 sec t, then the value of…

Question

Verified Solution • 2025–26 Session moderate

If x

=

3 tan t and y

=

3 sec t, then the value of

{{{d^2}y} \over {d{x^2}}}

at t

= {\pi \over 4},

is :

Accepted Answer

x = 3 tan t and y = 3 sec t

So that

{{dx} \over {dt}}

= 3sec²t and

{{dy} \over {dt}}

= 3 sec t tan t

{{dy} \over {dx}}

=

{{dy/dt} \over {dx/dt}}

= sin t

{{{d^2}y} \over {d{x^2}}}

= (cos t)

.{{dt} \over {dx}}

{{{d^2}y} \over {d{x^2}}} = \left( {\cos t} \right).{1 \over {3{{\sec }^2}t}}

{{{d^2}y} \over {d{x^2}}}

=

{1 \over 3}

(cos³ t)

{\left( {{{{d^2}y} \over {d{x^2}}}} \right)_{t = \pi /4}}

=

{1 \over 3} \times {\left( {{1 \over {\sqrt 2 }}} \right)^3} = {1 \over {6\sqrt 2 }}

QJEEM19Ma95ff: JEE Main 2019 Mathematics - Class 12 JEEM19Ma95ff Solution: If&nbsp;&nbsp;&nbsp;x 3 tan t and y 3 sec t, then the value of…