How to calculate the expression sin35*cos55+sin55*cos35?

This trigonometric sum returns the
formula:

sin x*cos y + sin y*cos x =
sin(x+y)

Let x = 35 and y =
55.

sin 35*cos 55 + sin 55*cos 35 =
sin(35+55)

sin 35*cos 55 + sin 55*cos 35 =
sin(90)

But sin 90 = 1, therefore the trigonometric sum
yields 1.

We notice that we'll use trigonometric
calculator, we'll get:

sin 55 = cos 35 =
0.8191...

sin 35 = cos 55 =
0.5735...

If we'll raise to square and then we'll add the
values, we'll get also 1.

Therefore, the
value of the trigonometric sum is sin 35*cos 55 + sin 55*cos 35 =
1.