Find the Exact Value (tan(45 degrees )+tan(60 degrees ))^2

Problem

(tan(45)+tan(60))2

Solution

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

tan(45)=1

tan(60)=√(,3)

2. Substitute these values into the original expression.

(1+√(,3))2

3. Expand the squared binomial using the formula (a+b)2=a2+2*a*b+b2

1+2*(1)*(√(,3))+(√(,3))2

4. Simplify the terms by calculating the squares and multiplying.

1+2√(,3)+3

5. Combine the constant terms to reach the final result.

4+2√(,3)

Final Answer

(tan(45)+tan(60))2=4+2√(,3)

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