$4 \,\,sin5^o \,\,sin55^o \,\,sin65^o$ =
$\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}$
$\frac{{\sqrt 3 - 1}}{{2\sqrt 2 }}$
$\frac{{\sqrt 3 - 1}}{{\sqrt 2 }}$
$\frac{{3\left( {\sqrt 3 - 1} \right)}}{{2\sqrt 2 }}$
જો $A + B + C = {180^o},$ તો $\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2} = . . .$
જો $A$ એ તૃતીય ચરણમાં હોય અને $3\ tanA - 4 = 0$ થાય તો $5\ sin\ 2A + 3\ sinA + 4\ cosA$ =
$\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) = $
$[1 - sin (3\pi - \alpha ) + cos (3\pi + \alpha )]$ $\left[ {1\,\, - \,\,\sin \,\left( {\frac{{3\,\pi }}{2}\,\, - \,\,\alpha } \right)\,\, + \,\,\cos \,\left( {\frac{{5\,\pi }}{2}\,\, - \,\,\alpha } \right)} \right]$ =
$(\sec 2A + 1){\sec ^2}A = $