કોઈ પણ $\theta \, \in \,\left( {\frac{\pi }{4},\frac{\pi }{2}} \right)$ માટે, $3\,{\left( {\sin \,\theta - \cos \,\theta } \right)^4} + 6{\left( {\sin \,\theta + \cos \,\theta } \right)^2} + 4\,{\sin ^6}\,\theta $ =
$13 - 4\,{\cos ^2}\,\theta \, + 6\,{\sin ^2}\,\theta \,{\cos ^2}\,\theta $
$13 - 4\,{\cos ^6}\,\theta \,$
$13 - 4\,{\cos ^2}\,\theta \, + 6\,\,{\cos ^4}\,\theta $
$13 - 4\,{\cos ^4}\,\theta \, + 2\,{\sin ^2}\,\theta \,{\cos ^2}\,\theta $
$\sin {163^o}\cos {347^o} + \sin {73^o}\sin {167^o} = $
$\sqrt {2 + \sqrt {2 + 2\cos 4\theta } } = $
જો $\tan x + \tan \left( {\frac{\pi }{3} + x} \right) + \tan \left( {\frac{{2\pi }}{3} + x} \right) = 3,$ તો
જો $cosA + cosB = cosC,\ sinA + sinB = sinC$ હોય તો સમીકરણ $\frac{{\sin \left( {A + B} \right)}}{{\sin 2C}}$ =
જો $\tan A = \frac{1}{2},\tan B = \frac{1}{3},$ તો $\cos 2A = $