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.