Simplify sin(pi/4)+cos(pi/4)

Problem

sin(π/4)+cos(π/4)

Solution

1. Evaluate the sine term using the unit circle or special right triangles, where sin(π/4)=√(,2)/2

2. Evaluate the cosine term using the unit circle or special right triangles, where cos(π/4)=√(,2)/2

3. Substitute these values back into the original expression.

√(,2)/2+√(,2)/2

4. Combine the fractions by adding the numerators over the common denominator.

(2√(,2))/2

5. Simplify the expression by canceling the common factor of 2 in the numerator and denominator.

√(,2)

Final Answer

sin(π/4)+cos(π/4)=√(,2)

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