$3\,\left[ {{{\sin }^4}\,\left( {\frac{{3\pi }}{2} – \alpha } \right) + {{\sin }^4}\,(3\pi + \alpha )} \right]$ $ – 2\,\left[ {{{\sin }^6}\,\left( {\frac{\pi }{2} + \alpha } \right) + {{\sin }^6}(5\pi – \alpha )} \right] = $

 $cotx – cosx = 1 – cotx. cosx$ માટે  $ x \in \left[ {0,2\pi } \right]$  ………… કિમતો મળે 

$\tan 5x\tan 3x\tan 2x = $

જો $\sin \theta  = \frac{1}{2}\left( {\sqrt {\frac{x}{y}\,}  + \,\sqrt {\frac{y}{x}} } \right)\,,\,\left( {x,y \in R\, – \{ 0\} } \right)$ થાય તો 

સાબિત કરો કે : $\cot 4 x(\sin 5 x+\sin 3 x)=\cot x(\sin 5 x-\sin 3 x)$