Prove:
sin (pi/4 + x) = sqrt2/2 (cos x + sin x)

Apply the angle sum identity .

Step-by-step explanation:

By the angle sum identity, for any angles and .

Apply this identity to rewrite the left-hand side of the equation:

.

The angle is equivalent to , which corresponds to the isosceles right triangle: , .

Substitute these two values into the expression above and simplify:

.

Thus, as requested.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80