State true or false- cos 24- cos 55- cos 125- cos 204- cos 300-12

The correct option is A TrueGiven #160;LHS #160; cos 24+cos 55+cos 125+cos 204+cos 300 cos 24+cos 55+cos (180 55)+cos(180+24)+cos(360 60) cos ...

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Composite Function

State true or...

Question

State true or false.
$cos 24^{\circ} + cos 55^{\circ} + cos 125^{\circ} + cos 204^{\circ} + cos 300^{\circ} = \frac{1}{2}$

True

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False

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Solution

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cos 24^{\circ} + cos 55^{\circ} + cos 125^{\circ} + cos 204^{\circ} + cos 300^{\circ}

cos 24^{o} + cos 55^{o} + cos 125^{o} + cos 204^{o} + cos 300^{o} = \frac{1}{2}

\sin \frac{8 π}{3} \cos \frac{23 π}{6} + \cos \frac{13 π}{3} \sin \frac{35 π}{6} = \frac{1}{2}

\frac{1}{2}

\tan \frac{11 π}{3} - 2 \sin \frac{4 π}{6} - \frac{3}{4} {cosec}^{2} \frac{π}{4} + 4 \cos^{2} \frac{17 π}{6} = \frac{3 - 4 \sqrt{3}}{2}

3 \sin \frac{π}{6} \sec \frac{π}{3} - 4 \sin \frac{5 π}{6} \cot \frac{π}{4} = 1

c o s (24^{o}) + c o s (5^{o}) + c o s (175^{o}) + c o s (204^{o}) + c o s (300^{o})

{(\frac{tan 60^{0} + 1}{tan 60^{0} - 1})}^{2} = \frac{1 + cos 30^{0}}{1 - cos 30^{0}}

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