Evaluate (tan(45 degrees )+tan(60 degrees ))^2

Problem

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

Solution

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

2. Substitute the value tan(45)=1 into the expression.

3. Substitute the value tan(60)=√(,3) into the expression.

4. Expand the squared binomial (1+√(,3))2 using the formula (a+b)2=a2+2*a*b+b2

5. Simplify the resulting terms by adding the constants.

Final Answer

(tan(45)+tan(60))2=4+2√(,3)

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