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=a^2+2*a*b+b^2

5. Simplify the resulting terms by adding the constants.

Final Answer

(tan(45^∘)+tan(60^∘))^2=4+2√(,3)

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