What is sqrt((4tan(θ))^2+16) ?

The solution to sqrt((4tan(θ))^2+16) is 4sqrt(sec^2(θ))

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simplify sqrt((4tan(θ))^2+16)

simplify

(4 tan (θ))^{2} + 16

4 sec^{2} (θ)

Solution steps

(4 tan (θ))^{2} + 16

Apply exponent rule:

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

= 4^{2} tan^{2} (θ) + 16

4^{2} = 16

= 16 + 16 tan^{2} (θ)

Factor

16 + 16 tan^{2} (θ) : 16 (1 + tan^{2} (θ))

= 16 (1 + tan^{2} (θ))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 16 tan^{2} (θ) + 1

16 = 4

= 4 tan^{2} (θ) + 1

Rewrite using trig identities

= 4 sec^{2} (θ)

1 + cot^{2} (- θ)

tan^{3} (arcsec (\frac{x}{3}))

tan (arccos (\frac{x}{13}))

- cos^{3} (18 0^{\circ} + X)

cos (2 t + 2 π)

What is sqrt((4tan(θ))^2+16) ?
The solution to sqrt((4tan(θ))^2+16) is 4sqrt(sec^2(θ))