What is sqrt((2sec(θ))^2-4) ?

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

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simplify sqrt((2sec(θ))^2-4)

simplify

(2 sec (θ))^{2} - 4

2 tan^{2} (θ)

Solution steps

(2 sec (θ))^{2} - 4

Apply exponent rule:

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

= 2^{2} sec^{2} (θ) - 4

Factor

2^{2} sec^{2} (θ) - 4 : 4 (sec^{2} (θ) - 1)

= 4 (sec^{2} (θ) - 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 4 sec^{2} (θ) - 1

4 = 2

= 2 sec^{2} (θ) - 1

Rewrite using trig identities

= 2 tan^{2} (θ)

tan (arcsin (5 x))

csc (arctan (2 x + 1))

sin (arccos (u))

2 sin (2 x - \frac{π}{4}) + 1

- sin (\cdot (- sin (x)))

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