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If $x=60^\circ$ and $y=45^\circ$ calculate, without using a calculator, the value of $\dfrac{1}{2}\cos{2x} - 2\sin{4y}$
in Grade 12 Maths by Diamond (40.2k points) | 13 views

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$=1/2*\cos(2*60) - 2*\sin(4*45) $

$=1/2*\cos(120) - 2*\sin(180) $

$=1/2*\cos(90 + 30) - 2* \sin(90 + 90) $

$=1/2* -\sin(30) - 2* \cos(90) $

$=1/2* -1/2 - 2*0 = -1/4$
by (103 points)
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Substituting,

$= \dfrac{1}{2} \times \cos{2(60)} - 2\sin{4(45)}$

$= \dfrac{1}{2} \times \cos{ 120} - 2\sin{180}$

$= \dfrac{1}{2} \times (-\cos{60} -2(0)$

$= \dfrac{1}{2} \times - \dfrac{1}{2} - 0$

$= -\dfrac{1}{4}$
by Silver Status (31.3k points)
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