JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the angle made by the tangent at the point \(\left(x_{0}, y_{0}\right)\) on the curve \(x=12(t+\sin t \cos t)\), \(y =12(1+\sin t )^{2}, 0 < t < \frac{\pi}{2}\), with the positive \(x\)-axis is \(\frac{\pi}{3}\), then \(y _{0}\) is equal to
- A \(6(3+2 \sqrt{2})\)
- B \(3(7+4 \sqrt{3})\)
- C \(27\)
- D \(48\)
Answer & Solution
Correct Answer
(C) \(27\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}=\frac{2(1+\sin t) \times \cos t}{1+\cos 2 t}\) \(\Rightarrow \frac{2(1+\sin t) \cos t}{2 \cos ^{2} t}=\sqrt{3}\) \(\Rightarrow t =\frac{\pi}{6}, y _{0}=27\)
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