Show that -Cos24-Cos55-Cos125-Cos204-Cos300-1-2

To prove that :Cos24^°+Cos55^°+Cos125^°+Cos204^°+Cos300^°=1/2L.H.S = Cos24^°+Cos55^°+Cos125^°+Cos204^°+Cos300^° = Cos24^°+Cos55^°+Cos (180^° 55^°)+Co ...

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Standard VII

Mathematics

Angle Sum Property

Show that :Co...

Question

Show that : $Cos 24^{°} + Cos 55^{°} + Cos 125^{°} + Cos 204^{°} + Cos 300^{°} = \frac{1}{2}$

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Solution

To prove that : $Cos 24^{°} + Cos 55^{°} + Cos 125^{°} + Cos 204^{°} + Cos 300^{°} = \frac{1}{2}$
$L . H . S$ $= Cos 24^{°} + Cos 55^{°} + Cos 125^{°} + Cos 204^{°} + Cos 300^{°}$
$= Cos 24^{°} + Cos 55^{°} + Cos (180^{°} - 55^{°}) + Cos (180^{°} + 24^{°}) + Cos (270^{°} + 30^{°})$
$= Cos 24^{°} + Cos 55^{°} - Cos 55^{°} - Cos 24^{°} + Sin 30^{°} [∵ \cos (180 ° - x) = - \cos x, \cos (180 ° + x) = - \cos x, \cos (270 ° + x) = \sin x]$
$= Sin 30^{°}$
$= \frac{1}{2}$
$= RHS$
Thus, $Cos 24^{°} + Cos 55^{°} + Cos 125^{°} + Cos 204^{°} + Cos 300^{°} = \frac{1}{2}$ .
Hence proved.

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Similar questions

Q. If

4 x - 4 x^{- 1} = 24,

then (2x)^x equals

(a)

5 \sqrt{5}

(b)

\sqrt{5}

(c)

25 \sqrt{5}

(d) 125

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

State true or false.

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

Q. Find the value of

cos 24^{o} + cos 55^{o} + cos 125^{o} + cos 204^{o} + cos 300^{o}

Q. The value of

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

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Show that :Cos24°+Cos55°+Cos125°+Cos204°+Cos300°=12

Show that : $Cos 24^{°} + Cos 55^{°} + Cos 125^{°} + Cos 204^{°} + Cos 300^{°} = \frac{1}{2}$