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

If \[\mathbf{cos}\alpha =\mathbf{sin14}\,\alpha \] (where \[\mathbf{0}

1.	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
Answer» D. \[\sqrt{2}+1\]

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