જો $A + B + C = \pi ,$ તો $\cos \,\,2A + \cos \,\,2B + \cos \,\,2C = $

$\frac{{\tan \,\,\left( {x\,\, - \,\,{\textstyle{\pi  \over 2}}} \right)\,\,.\,\,\cos \,\,\left( {{\textstyle{{3\pi } \over 2}}\,\, + \,\,x} \right)\,\, - \,\,{{\sin }^3}\,\left( {{\textstyle{{7\pi } \over 2}}\,\, - \,\,x} \right)}}{{\cos \,\,\left( {x\,\, - \,\,{\textstyle{\pi  \over 2}}} \right)\,\,.\,\,\tan \,\,\left( {{\textstyle{{3\pi } \over 2}}\,\, + \,\,x} \right)}}$  = 

$\cos 2(\theta + \phi ) - 4\cos (\theta + \phi )\sin \theta \sin \phi + 2{\sin ^2}\phi = $

$\sin 600^\circ \cos 330^\circ + \cos 120^\circ \sin 150^\circ   =....$

જો $x = sec\, \phi - tan\, \phi$ & $y = cosec\, \phi + cot\, \phi$ હોય તો, 

સમીકરણ ${\sin ^2}\,2\theta  + {\cos ^4}\,2\theta  = \frac{3}{4}$ ના $\theta \, \in \,\left( {0,\frac{\pi }{2}} \right)$ ના બધા ઉકેલો નો સરવાળો .......... થાય.