8-1. Find the extreme values of cos...
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8-1. Find the extreme values of cos x cos( 2 x cos( 35 - x)

JEE/Engineering Exams
Maths
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( cos (A+B) cdot cos (A-B)=cos ^{2} A-sin ^{2} B ) ( therefore cos left(frac{2 pi}{3}+xright) cos left(frac{pi pi}{3}-xright)=cos ^{2}left(frac{pi pi}{3}right)-sin ^{2}(x) ) -2 ( begin{aligned} &=frac{1}{4}-sin ^{2} x &=frac{1}{4}-1+cos ^{2} x=-frac{3}{4}+cos 2 x therefore cos xleft(frac{-3}{4}+cos ^{2} xright)=& frac{-3}{4} cos x+cos ^{3} x &=frac{-3 cos x+4 cos ^{3} x}{4} -frac{1}{4} leq frac{1}{4} &=frac{cos 3 x}{4} &=frac{10 x}{4} end{aligned} )
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