Evaluate sin(45 degrees )^2+cos(30 degrees )^2

Problem

sin(45)+cos(30)

Solution

1. Identify the exact values for the trigonometric functions at the given angles.

2. Substitute the value sin(45)=√(,2)/2 into the expression.

3. Substitute the value cos(30)=√(,3)/2 into the expression.

4. Square the first term:

(√(,2)/2)2=2/4=1/2

5. Square the second term:

(√(,3)/2)2=3/4

6. Add the two resulting fractions by finding a common denominator:

1/2+3/4=2/4+3/4=5/4

Final Answer

sin(45)+cos(30)=5/4

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