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  • explain solution RD Sharma class 12 chapter Derivative As a Rate Measure exercise 12.2 question 16 sub question (i) maths

explain solution RD Sharma class 12 chapter Derivative As a Rate Measure exercise 12.2 question 16 sub question (i) maths

Answers (1)

Answer: \frac{7\pi }{6}

Hint: Here we use the formula of angles

Given: \frac{d \theta}{d t}=2 \times \frac{d(\cos \theta)}{d t}

Solution:

\begin{aligned} &\frac{d \theta}{d t}=2 \times \frac{d(\cos \theta)}{d t} \\\\ &\frac{d \theta}{d t}=2 \times \frac{d(\cos \theta)}{d \theta} \times \frac{d \theta}{d t} \end{aligned}

\begin{aligned} &1=2(-\sin \theta) \\\\ &\sin \theta=-\frac{1}{2} \end{aligned}

 Hence, \theta=\frac{7 \pi}{6}

So the value of angle \theta  which increases twice as fast as its cosine is \frac{7\pi }{6}

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