JEE MATHEMATICS MCQ: DIFFERENTIAL EQUATIONS

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Analyzing +4 | -1

Let

x(t)=2 \sqrt{2} \cos t \sqrt{\sin 2 t}

and

y\left( t \right) = 2\sqrt 2 \sin t\sqrt {\sin 2t} ,\,\,\,t \notin \left( {0,\frac{\pi }{2}} \right).

Then

\frac{{1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}}}{{\frac{{{d^2}y}}{{d{x^2}}}}}\,at\,\,t = \frac{\pi }{4}

is eqaul to

View answer and explanation

Correct option: D

\frac{{ - 2}}{3}

Option D (-2/3) is correct because after finding the first and second derivatives and substituting t = pi/4, the expression evaluates to -2/3.

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