It is said to convert the expression in a single angle single function.
The given expression is:
[tex]\sin 20^{\circ}\cos 30^{\circ}+\cos 20^{\circ}\sin 30^{\circ}[/tex]It is known that:
[tex]\sin (A+B)=\sin A\cos B+\cos A\sin B[/tex]Apply the formula in reverse to get:
[tex]\sin A\cos B+\cos A\sin B=\sin (A+B)[/tex]Hence the given expression can be written as:
[tex]\sin 20^{\circ}\cos 30^{\circ}+\cos 20^{\circ}\sin 30^{\circ}=\sin (20^{\circ}+30^{\circ})=\sin 50^{\circ}[/tex]Hence the vaue of the expression is sin50 degrees.
