What is sqrt((6sec(θ))^2-36) ?

The solution to sqrt((6sec(θ))^2-36) is 6sqrt(tan^2(θ))

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simplify sqrt((6sec(θ))^2-36)

simplify

(6 sec (θ))^{2} - 36

6 tan^{2} (θ)

Solution steps

(6 sec (θ))^{2} - 36

Apply exponent rule:

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

= 6^{2} sec^{2} (θ) - 36

Factor

6^{2} sec^{2} (θ) - 36 : 36 (sec^{2} (θ) - 1)

= 36 (sec^{2} (θ) - 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 36 sec^{2} (θ) - 1

36 = 6

= 6 sec^{2} (θ) - 1

Rewrite using trig identities

= 6 tan^{2} (θ)

csc (arcsin (\frac{x}{5}))

sin (cos (- 1 x))

sec (x) cos (\frac{π}{2} - x)

cos (a rc i s n (- \frac{4}{13}))

csc (arccot (\frac{16}{x}))

What is sqrt((6sec(θ))^2-36) ?
The solution to sqrt((6sec(θ))^2-36) is 6sqrt(tan^2(θ))