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  • The value of  <img alt="\mathrm{2\sin\left ( 12^{\circ} \right )-\sin\left ( 72^{\circ} \right )}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B2%5Csin%5Cleft%20%28%2012%5E

The value of  \mathrm{2\sin\left ( 12^{\circ} \right )-\sin\left ( 72^{\circ} \right )} is :

Option: 1

\mathrm{\frac{\sqrt{5}\left ( 1-\sqrt{3} \right )}{4}}


Option: 2

\mathrm{\frac{1-\sqrt{5}}{8}}


Option: 3

\mathrm{\frac{\sqrt{3}\left ( 1-\sqrt{5} \right )}{2}}


Option: 4

\mathrm{\frac{\sqrt{3}\left ( 1-\sqrt{5} \right )}{4}}


Answers (1)

best_answer

To find

\mathrm{\Rightarrow 2\sin12^{{\circ}}-\sin72^{\circ} }

\mathrm{\Rightarrow \sin 12^{\circ}+\sin 12^{\circ}-\sin 72^{\circ}} \\

\mathrm{\Rightarrow \sin 12^{\circ}+2 \cos 42^{\circ} \sin \left(-30^{\circ}\right) \Rightarrow \sin 12^{\circ}-\cos 42^{\circ}} \\

\mathrm{\Rightarrow \sin 12^{\circ}-\sin 4 8^{\circ} }\\

\mathrm{\Rightarrow 2 \cos \left(30^{\circ}\right) \sin \left(-18^{\circ}\right) }

\mathrm{\Rightarrow -\sqrt{3}\sin 18^{\circ} }

\mathrm{\Rightarrow -\sqrt{3}\left ( \frac{\sqrt{5}-1}{4} \right )=\sqrt{3}\left ( \frac{1-\sqrt{5}}{4} \right ) }

Hence the correct answer is option 4

Posted by

rishi.raj

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