What is sqrt((2tan(θ))^2+4) ?

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

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simplify sqrt((2tan(θ))^2+4)

simplify

(2 tan (θ))^{2} + 4

2 sec^{2} (θ)

Solution steps

(2 tan (θ))^{2} + 4

Apply exponent rule:

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

= 2^{2} tan^{2} (θ) + 4

Factor

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

= 4 (tan^{2} (θ) + 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 4 tan^{2} (θ) + 1

4 = 2

= 2 tan^{2} (θ) + 1

Rewrite using trig identities

= 2 sec^{2} (θ)

sin (27 0^{\circ} + A)

x^{2} + 5 x + 2 = - 4

3 x^{2} + (k + 1) x - 2 = 0

x, x^{2} - k x + 64 = 0

(3 - x)^{2} + x^{2} = 2 (5 - x)

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