Simplify (1+tan(x))^2

Problem

(1+tan(x))^2

Solution

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

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

2. Simplify the terms by performing the multiplication.

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

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

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

4. Apply the Pythagorean identity 1+tan^2(x)=sec^2(x) to simplify the expression further.

(1+tan(x))^2=sec^2(x)+2*tan(x)

Final Answer

(1+tan(x))^2=sec^2(x)+2*tan(x)

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