What is the sum of functions sin 135+cos150? please explain the sum

We notice that 135 = 90 + 45 and 150 = 90 +
60

We'll use the trigonometric
identities:

sin(a+b) = sin a*cos b + sin b*cos
a

cos (a+b) = cos a*cos b - sin a*sin
b

According to all of these, we'll
have:

sin 135 = sin (90 + 45) = sin 90*cos 45 + sin 45*cos
90

We'll have sin 90 = 1 ; cos 45 = sin 45 = sqrt2/2 and
cos 90 = 0

sin 135 =
sqrt2/2

cos 150 = cos (90 + 60) = cos 90*cos60 -
sin90*sin60

cos 90 = 0, sin 90 = 1, cos 60 = 1/2, sin 60 =
sqrt3/2

cos 150 =
-sqrt3/2

The value of the sum is sin 135+cos
150 = (sqrt2 - sqrt3)/2.