Question

Write the value of 

\[\begin{vmatrix}\sin 20^\circ & - \cos 20^\circ\\ \sin 70^\circ& \cos 70^\circ\end{vmatrix}\]

Answer 1

\[\text{ Let }\Delta = \begin{vmatrix} \sin 20^\circ & - \cos 20^\circ\\\sin 70^\circ & \cos 70^\circ \end{vmatrix}\] 
\[ = \sin 20^\circ \cos 70^\circ + \cos 20^\circ\sin 70^\circ\] 
\[ = \sin (20^\circ + 70^\circ) \left[\text{ trignometric identity }\right]\] 
\[ = \sin 90^\circ \] 
\[ = 1\]