Solve 1=2asin(pi/6)cos(-pi/3)

$$1 = 2a \sin ( \frac{ \pi }{ 6 } ) \cos ( - \frac{ \pi }{ 3 } )$$

Solve for a

$$a=2$$

Steps for Solving Linear Equation

Get the value of \sin(\frac{\pi }{6}) from trigonometric values table.

$$1=2a\times \frac{1}{2}\cos(-\frac{\pi }{3})$$

Multiply 2 and \frac{1}{2} to get 1.

$$1=a\cos(-\frac{\pi }{3})$$

Swap sides so that all variable terms are on the left hand side.

$$a\cos(-\frac{\pi }{3})=1$$

The equation is in standard form.

$$\cos(-\frac{\pi }{3})a=1$$

Divide both sides by \cos(-\frac{1}{3}\pi ).

$$\frac{\cos(-\frac{\pi }{3})a}{\cos(-\frac{\pi }{3})}=\frac{1}{\cos(-\frac{\pi }{3})}$$

Dividing by \cos(-\frac{1}{3}\pi ) undoes the multiplication by \cos(-\frac{1}{3}\pi ).

$$a=\frac{1}{\cos(-\frac{\pi }{3})}$$

Divide 1 by \cos(-\frac{1}{3}\pi ).

$$a=2$$