4 19. Minimum value of the expressi...
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4 19. Minimum value of the expression cos206 sin cos 0) + 3 sin? 0 + 2, is - (A) 4+ V10 (B) 4-V50 (c)0 (D) 4 ina nyin CITY

JEE/Engineering Exams
Maths
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( begin{aligned} & cos ^{2} theta-(6 sin theta cos theta)+3 sin ^{2} theta+2 =& cos ^{2} theta+sin ^{2} theta-3 sin 2 theta+2 sin ^{2} theta+2 =& 1-3 sin 2 theta+1-cos 2 theta+2 =& 4-38 sin 2 theta-cos 2 theta =& 4-sqrt{10} cdotleft(frac{3}{sqrt{10}} sin 2 theta+frac{1}{sqrt{10}} cos 20right) =& 4-sqrt{10}(sin (2 theta+alpha)) =& 4-sqrt{10} cdot(-1) cdot frac{cdot-1 leq 8 operatorname{in} 2 theta+alpha leq 1}{1} =& 4+sqrt{10} end{aligned} )
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