What is sqrt((2sec(x))^2-4) ?

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

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simplify sqrt((2sec(x))^2-4)

simplify

(2 sec (x))^{2} - 4

2 tan^{2} (x)

Solution steps

(2 sec (x))^{2} - 4

Apply exponent rule:

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

= 2^{2} sec^{2} (x) - 4

Factor

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

= 4 (sec^{2} (x) - 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 4 sec^{2} (x) - 1

4 = 2

= 2 sec^{2} (x) - 1

Rewrite using trig identities

= 2 tan^{2} (x)

\frac{d y}{cot ( y )}

sec (π + x)

(- cos (- \frac{π}{4} + x))^{2}

cos (\frac{x}{- 3})

1 + cos (\frac{π}{2} - x)

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