What is sqrt(2^2+(2tan(t))^2) ?

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

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simplify sqrt(2^2+(2tan(t))^2)

simplify

2^{2} + (2 tan (t))^{2}

2 sec^{2} (t)

Solution steps

2^{2} + (2 tan (t))^{2}

Apply exponent rule:

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

= 2^{2} + 2^{2} tan^{2} (t)

Factor

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

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

4 = 2

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

Rewrite using trig identities

= 2 sec^{2} (t)

cos (12 0^{\circ} - t)

sin (\frac{2}{cos ( 7 x )})

tan (θ - 36 0^{\circ})

y e^{2} cos (6 \cdot (- 3))

1 - sin^{2} (X)

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