question_answer

If \[\mathbf{cos}\alpha =\mathbf{sin14}\,\alpha \] (where \[\mathbf{0}{}^\circ \mathbf{< 14}\alpha \mathbf{< 90{}^\circ }\]), then find the value of \[\mathbf{sin5}\alpha \mathbf{+cos}\left( \mathbf{12}\alpha -\mathbf{ 27{}^\circ } \right)\]\[-\,\mathbf{cosec}\left( \mathbf{3}\alpha \mathbf{+ 12{}^\circ } \right).\]

A)  \[\sqrt{2}\]                                                                   

B)  \[\sqrt{2}-1\]      

C)  \[\frac{\sqrt{2}-1}{2}\]   

D)  \[\sqrt{2}+1\]

E) None of these