Express the following as a function of a single angle sin 20 degree cos 30 degree + cos 20 degree sin 30 degree
To express the expression sin 20° cos 30° + cos 20° sin 30° as a function of a single angle, we can use the trigonometric identity for the sum of angles:
sin(A + B) = sin A cos B + cos A sin B
Let's rewrite the given expression using the above identity:
sin 20° cos 30° + cos 20° sin 30°
= sin(20° + 30°)
We can simplify the angle 20° + 30° to 50°. So, the given expression can be expressed as a function of a single angle:
sin(50°)
do you recall that
sin(A+B) = sinAcosB + cosAsinB?
Does that look familiar?