दिया है  $\sin 2\,\theta  + \sin 2\phi  = 1/2$…..$(i)$

एवं $\cos 2\,\theta  + \cos 2\,\phi  = 3/2$…..$(ii)$

वर्ग करके जोड़ने पर,

$\therefore \,({\sin ^2}2\theta  + {\cos ^2}2\theta ) + ({\sin ^2}2\phi  + {\cos ^2}2\phi  )$

$ + 2\,[\sin 2\,\theta \,\sin 2\,\phi  + \cos 2\,\theta \,\cos 2\,\phi  ] = (1/4) + (9/4)$

$\Rightarrow$ $\cos 2\theta \cos 2\,\phi  + \sin 2\theta \sin 2\phi  = 1/4$

$\Rightarrow$ $\cos (2\theta  – 2\phi  ) = 1/4$

$\Rightarrow$  ${\cos ^2}(\theta  – \phi   ) = 5/8$.