Nilai dari =........... a. b. 1/2 akar3 c. 1/3 akar3 d. -1/2 akar3 e.

October 2018 2 139 Report

Nilai dari
$\frac{sin 81+sin 21}{sin 69 - sin 171}$ =...........

a. $\sqrt{3}$
b. 1/2 akar3
c. 1/3 akar3
d. -1/2 akar3
e. - akar3

Takamori37 Rumus bantuan:
$\boxed{\sin A+\sin B=2\sin\frac{A+B}{2}\cos\frac{A-B}{2}} \\\\ \boxed{\sin A-\sin B=2\cos\frac{A+B}{2}\sin\frac{A-B}{2}}$

Maka,
$$\begin{align}\frac{\sin81+\sin21}{\sin69-\sin171}&=\frac{\not{2}\sin\frac{81+21}{2}\cos\frac{81-21}{2}}{\not{2}\cos\frac{69+171}{2}\sin\frac{69-171}{2}} \\ &=\frac{\sin51\cos30}{\cos120\sin(-51)} \\ &=\frac{\sin51\cos30}{\cos(180-60)\sin(0-51)} \\ &=\frac{\sin51\cos30}{-\cos60\times-\sin51} \\ &=\frac{\cos30}{\cos60} \\ &=\frac{\frac{1}{2}\sqrt{3}}{\frac{1}{2}} \\ &=\sqrt{3}\ \ [A]\end{align}$

12 votes Thanks 18

alvinteguh $\displaystyle \frac{2.sin \frac{81 + 21}{2}. cos \frac{81 - 21}{2} }{cos 21 - cos 81} = \frac{2.sin \frac{102}{2}.cos \frac{60}{2} }{-2 . sin \frac{21 + 81}{2} . sin \frac{21 - 81}{2} } \\ = \frac{2.sin 51 . cos 30}{-2 . sin \frac{102}{2}. sin \frac{-60}{2} } = \frac{2.sin 51.cos 30}{-2 . sin 51.sin(-30)} \\ = \frac{2.sin 51 . cos 30}{-2.sin 51 . (- \frac{1}{2}) } = \frac{2. cos 30}{1} = 2.cos 30 = 2.( \frac{1}{2} \sqrt{3} ) = \sqrt{3}$

2 votes Thanks 5

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