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  • The value of sin⁡〖π/18〗+sin⁡〖π/9〗+sin⁡〖2π/9〗+sin⁡〖5π/18〗 is given by A.sin⁡〖4π/9〗+sin⁡〖7π/18〗

The value of \sin \frac{\pi}{18}+\sin \frac{\pi}{9}+\sin \frac{2 \pi}{9}+\sin \frac{5 \pi}{18} is given by

\\A. \sin \frac{7 \pi}{18}+\sin \frac{4 \pi}{9}\\\\ B .1\\\\ C \cdot \cos \frac{\pi}{6}+\cos \frac{3 \pi}{7}\\\\ D \cdot \cos \frac{\pi}{9}+\sin \frac{\pi}{9}

Answers (1)

The answer is the option (a). 

\\\\ \sin \frac{ \pi }{18}+\sin \frac{ \pi }{9}+\sin \frac{2 \pi }{9}+\sin \frac{5 \pi }{18}= \left( \sin \frac{ \pi }{18}+\sin \frac{5 \pi }{18} \right) + \left( \sin \frac{ \pi }{9}+\sin \frac{2 \pi }{9} \right) \\\\ =2\sin \frac{\frac{5 \pi }{18}+\frac{ \pi }{18}}{2}\cos \frac{\frac{5 \pi }{18} - \frac{ \pi }{18}}{2}+2\sin \frac{\frac{ \pi }{9}+\frac{2 \pi }{9}}{2}\cos \frac{\frac{2 \pi }{9} - \frac{ \pi }{9}}{2} \\\\ =2\sin \frac{ \pi }{6}\cos \frac{ \pi }{9}+2\sin \frac{ \pi }{6}\cos \frac{ \pi }{18}=2 \times \frac{1}{2}\cos \frac{ \pi }{9}+2 \times \frac{1}{2}\cos \frac{ \pi }{18} \\\\ =\cos \frac{ \pi }{9}+\cos \frac{ \pi }{18} \\\\ =\sin \left( \frac{ \pi }{2} - \frac{ \pi }{9} \right) +\sin \left( \frac{ \pi }{2} - \frac{ \pi }{18} \right) \\\\ =\sin \frac{4 \pi }{9}+\sin \frac{7 \pi }{18} \\\\

Hence, correct option is (a).

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infoexpert21

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