Question

If the angle made by the tangent at the point (x 0, y 0) on the curve x = 12(t + sin t cos t),

$y=12(1+sint)^2,0<t<\frac{π}{2},$

with the positive x -axis is π/3, then y 0 is equal to

• A. $6(3+2\sqrt2)$
• B. $3(7+4\sqrt3)$
• C. 27
• D. 48

Answer 1

Answer: (A)

$6(3+2\sqrt2)$

Answer 2

The correct option is(C): 27.

$∵\frac{dy}{dx}=\frac{24(1+sint)cost}{12(1+cos2t)}$

$=\frac{1+sint}{cost}=tan(\frac{\pi}{4}+\frac{t}{2})$

$t=\frac{\pi}{6}$

So,

$y_0(at\,t\frac{\pi}{6}=12(1+sin\frac{\pi}{6})^2=27.$