$\frac{{4\sin {9^o}\sin {{21}^o}\sin {{39}^o}\sin {{51}^o}\sin {{69}^o}\sin {{81}^o}}}{{\sin {{54}^o}}}$ =
$\frac{1}{16}$
$\frac{1}{32}$
$\frac{1}{8}$
$\frac{1}{4}$
$\left( {1 + \cos \frac{\pi }{8}} \right)\,\left( {1 + \cos \frac{{3\pi }}{8}} \right)\,\left( {1 + \cos \frac{{5\pi }}{8}} \right)\,\left( {1 + \cos \frac{{7\pi }}{8}} \right) = $
$cosec \frac{\pi }{{18}} - \sqrt 3 \,sec\, \frac{\pi }{{18}}$ =
સાબિત કરો કે : $\frac{\cos 4 x+\cos 3 x+\cos 2 x}{\sin 4 x+\sin 3 x+\sin 2 x}=\cot 3 x$
જો ${\cos ^6}\alpha + {\sin ^6}\alpha + K\,{\sin ^2}2\alpha = 1,$ તો $K =$
જો $\alpha $ અને $\beta $ એ સમીકરણ $sin^2\,x + a\, sin\, x + b = 0$ અને $cos^2\,x + c\, cos\, x + d = 0$ ના બીજો હોય તો $sin\,(\alpha + \beta )$ =