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Geometry Level 3

sin ⁡ ( π 10 ) + sin ⁡ ( 13 π 10 ) = X \large\sin\left(\dfrac{\pi}{10}\right)+\sin\left(\dfrac{13\pi}{10}\right) = X

Find the value of X X .


The answer is -0.5.

Krishna Shankar by Krishna Shankar , 23, India

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1 solution

Akshat Sharda
Oct 7, 2015

sin ⁡ π 10 + sin ⁡ 13 π 10 = sin ⁡ π 10 − sin ⁡ 3 π 10 \sin \frac{\pi}{10}+\sin \frac{13\pi}{10} =\sin \frac{\pi}{10}-\sin \frac{3\pi}{10}

sin ⁡ 18 ° − sin ⁡ 54 ° = 5 − 1 4 − 5 + 1 4 \sin 18°-\sin 54°=\frac{\sqrt{5}-1}{4}-\frac{\sqrt{5}+1}{4}

− 1 2 = − 0.5 -\frac{1}{2}=\boxed{-0.5}

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