What is expand (1+tan(x/2))^2 ?

The solution to expand (1+tan(x/2))^2 is sec^2(x/2)+2tan(x/2)

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expand (1+tan(x/2))^2

expand

(1 + tan (\frac{x}{2}))^{2}

sec^{2} (\frac{x}{2}) + 2 tan (\frac{x}{2})

Solution steps

(1 + tan (\frac{x}{2}))^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(1 + tan (\frac{x}{2}))^{2} = 1^{2} + 2 \cdot 1 \cdot tan (\frac{x}{2}) + tan^{2} (\frac{x}{2})

= 1^{2} + 2 \cdot 1 \cdot tan (\frac{x}{2}) + tan^{2} (\frac{x}{2})

Simplify

1^{2} + 2 \cdot 1 \cdot tan (\frac{x}{2}) + tan^{2} (\frac{x}{2}) : sec^{2} (\frac{x}{2}) + 2 tan (\frac{x}{2})

= sec^{2} (\frac{x}{2}) + 2 tan (\frac{x}{2})

A (2, - 7) y

21 (1 - e^{(- 0.04 t)})

(x - \frac{1}{2})^{2} - 1

\frac{( 5 - x ) \cdot 2}{13}

What is expand (1+tan(x/2))^2 ?
The solution to expand (1+tan(x/2))^2 is sec^2(x/2)+2tan(x/2)