Move the term outside of the limit because it is constant with respect to .

Move the limit inside the trig function because sine is continuous.

Split the limit using the Sum of Limits Rule on the limit as approaches .

Move the limit inside the trig function because sine is continuous.

Evaluate the limit of by plugging in for .

Evaluate the limit of by plugging in for .

Simplify each term.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of is .

Add and .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of is .

Multiply by .

Evaluate limit as x approaches pi of 4sin(x+sin(x))