How to calculate the expression sin105*cos45-sin45*cos105?

To evaluate the given expression, we'll use the
identity:

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

Let x = 105 and y = 45

We'll
re-write the given difference:

sin 105*cos 45 - sin 45*cos
105 = sin (105 - 45)

sin 105*cos 45 - sin 45*cos 105 = sin
60

But sin 60 = (sqrt
3)/2

Therefore, the value of the given
expression is sin 105*cos 45 - sin 45*cos 105 = (sqrt
3)/2.