Simplify (1+tan(x))^2

Problem

(1+tan(x))2

Solution

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

(1+tan(x))2=1+2*(1)*(tan(x))+tan2(x)

2. Simplify the terms by performing the multiplication.

(1+tan(x))2=1+2*tan(x)+tan2(x)

3. Rearrange the terms to group the constant and the squared trigonometric function.

(1+tan(x))2=1+tan2(x)+2*tan(x)

4. Apply the Pythagorean identity 1+tan2(x)=sec2(x) to simplify the expression further.

(1+tan(x))2=sec2(x)+2*tan(x)

Final Answer

(1+tan(x))2=sec2(x)+2*tan(x)

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