Find an angle  which increases twice as fast as its cosine.

Explanation

Let `x=cos theta`


Differentiating both sides with respect to `t`, we get `frac{d x}{d t}=frac{d(cos theta)}{d t}` `=-sin theta frac{d theta}{d t}`
But it is given that `frac{d theta}{d t}=2 frac{d x}{d t}` `Rightarrow frac{d x}{d t}=-sin theta(2 frac{d x}{d t})`



`Rightarrow sin theta=-frac{1}{2}`




`Rightarrow theta=pi+frac{pi}{6}=frac{7 pi}{6}`


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