Evaluate \( \begin{vmatrix} sin 60 ^\circ& cos 60^\circ\\[0.3em] -sin

1.	Evaluate \( \begin{vmatrix} sin 60 ^\circ& cos 60^\circ\\[0.3em] -sin 30^\circ & cos30^\circ \\[0.3em] \end{vmatrix}\) Evaluate \|(sin60°, cos60°) (-sin 30° cos 30°)\|
Answer» After finding determinant we will get, Sin60° = \(\frac{\sqrt{3}}{2}\) = cos 30° Cos60° = \(\frac{1}{2}\) = sin30° sin 60° × cos30° + sin30° × cos60° = \(\frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} + \frac{1}{2} \times \frac{1}{2}\) = \(\frac{3}{4} + \frac{1}{4}\) = 1.

Evaluate \( \begin{vmatrix} sin 60 ^\circ& cos 60^\circ\\[0.3em] -sin 30^\circ & cos30^\circ \\[0.3em] \end{vmatrix}\) Evaluate |(sin60°, cos60°) (-sin 30° cos 30°)|

Answer»

After finding determinant we will get,

Sin60° = \(\frac{\sqrt{3}}{2}\) = cos 30°

Cos60° = \(\frac{1}{2}\) = sin30°

sin 60° × cos30° + sin30° × cos60°

= \(\frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} + \frac{1}{2} \times \frac{1}{2}\)

= \(\frac{3}{4} + \frac{1}{4}\)

= 1.