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  • The value of sin⁡〖π/10〗 sin⁡〖13π/10〗 is A.1/2

The value of \sin \frac{ \pi }{10}\sin \frac{13 \pi }{10} is

A.\frac{1}{2}

B.-\frac{1}{2}

C.-\frac{1}{4}

D.1

 

Answers (1)

The answer is the option (c). 

 \\ \sin \frac{ \pi }{10}\sin \frac{13 \pi }{10}=\sin \frac{ \pi }{10}\sin \left( \pi +\frac{3 \pi }{10} \right) =\sin \frac{ \pi }{10} \left( - \sin \frac{3 \pi }{10} \right) \\\\ = - \sin 18\sin 54= - \left( \frac{\sqrt {5} - 1}{4} \right) \left( \frac{\sqrt {5}+1}{4} \right) \\\\ =\frac{5 - 1}{16}=\frac{4}{16}=\frac{1}{4} \\\\

Hence, (c) is correct option.  

Posted by

infoexpert21

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