माना $u = \cos \theta \left\{ {\sin \theta  + \sqrt {{{\sin }^2}\theta  + {{\sin }^2}\alpha } } \right\}$

$ \Rightarrow  {(u – \sin \theta \cos \theta )^2} = {\cos ^2}\theta ({\sin ^2}\theta  + {\sin ^2}\alpha )$

$ \Rightarrow {u^2}{\tan ^2}\theta  – 2u\tan \theta  + {u^2} – {\sin ^2}\alpha  = 0$

चूँकि $\tan \theta $ वास्तविक है।

अत: $4{u^2} – 4{u^2}({u^2} – {\sin ^2}\alpha ) \ge 0$

$ \Rightarrow {u^2} – (1 + {\sin ^2}\alpha ) \le 0$

$ \Rightarrow  |u|\, \le \sqrt {1 + {{\sin }^2}\alpha } $.