What is sqrt(4+(2tan(x))^2) ?

The solution to sqrt(4+(2tan(x))^2) is 2sqrt(sec^2(x))

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simplify sqrt(4+(2tan(x))^2)

simplify

4 + (2 tan (x))^{2}

2 sec^{2} (x)

Solution steps

4 + (2 tan (x))^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 4 + 2^{2} tan^{2} (x)

Factor

4 + 2^{2} tan^{2} (x) : 4 (1 + tan^{2} (x))

= 4 (1 + tan^{2} (x))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 4 tan^{2} (x) + 1

4 = 2

= 2 tan^{2} (x) + 1

Rewrite using trig identities

= 2 sec^{2} (x)

a r cot (\frac{3}{- 1})

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

sin (- 0.65 r a d)

sec (x + \frac{π}{5})

sec (arctan (\frac{y}{2}))

What is sqrt(4+(2tan(x))^2) ?
The solution to sqrt(4+(2tan(x))^2) is 2sqrt(sec^2(x))