# A trigonometric function !!!

Algebra Level pending

Find the range of the following function :-

$$f(\theta )\quad =\quad \sqrt { 8{ sin }^{ 2 }\theta +4cos^{ 2 }\theta -8{ sin }\theta cos\theta }$$

$$\bullet The\quad answer\quad can\quad be\quad expressed\quad in\quad the\quad form\quad of\quad \left[ \sqrt { A-\sqrt { B } } ,\sqrt { C+\sqrt { D } } \right] \quad where\quad B-A=14$$

$$\bullet Find\quad A+B+C+D$$

$$\bullet The\quad values\quad of\quad any\quad of\quad them\quad may\quad be\quad same\quad as\quad other.$$

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