Question

Write as a single function of asingle angle.Help Resourcesin 20° cos 30° + cos 20° sin 30º = ?

Answer 1

It is said to convert the expression in a single angle single function.

The given expression is:

$\sin 20^{\circ}\cos 30^{\circ}+\cos 20^{\circ}\sin 30^{\circ}$

It is known that:

$\sin (A+B)=\sin A\cos B+\cos A\sin B$

Apply the formula in reverse to get:

$\sin A\cos B+\cos A\sin B=\sin (A+B)$

Hence the given expression can be written as:

$\sin 20^{\circ}\cos 30^{\circ}+\cos 20^{\circ}\sin 30^{\circ}=\sin (20^{\circ}+30^{\circ})=\sin 50^{\circ}$

Hence the vaue of the expression is sin50 degrees.