The value of   \sin 10 ^{o}\sin 30 ^{o}\sin 50 ^{o}\sin 70 ^{o}  is :

  • Option 1)

    \frac{1}{16}

  • Option 2)

    \frac{1}{32}

  • Option 3)

    \frac{1}{18}

  • Option 4)

    \frac{1}{36}

 

Answers (1)
V Vakul

\\ \sin 10^{o} \sin 30^{o} \sin 50^{o}\sin 70\\\\\\\:\frac{1}{4}\sin 10^{o}\left ( 2\sin 50^{o}\sin 70^{o} \right )\\\\\\\:\frac{1}{4}\sin 10^{o}\left ( \cos 20^{o}-\cos 120^{o} \right )\\\\\\\:\frac{1}{8}\left ( 2\sin 10^{o}\cos 20^{o}-2 \sin10^{o}\cos 120^{o}\right )

\\\frac{1}{8}\left ( \sin 30^{o} -\sin10^{o}+\sin10^{o}\right )\\\\\\\:\frac{1}{8}\left ( \frac{1}{2} \right )=\frac{1}{16}


Option 1)

\frac{1}{16}

Option 2)

\frac{1}{32}

Option 3)

\frac{1}{18}

Option 4)

\frac{1}{36}

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