What is sqrt((-10sec(θ))^2-100) ?

The solution to sqrt((-10sec(θ))^2-100) is 10tan(θ)

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simplify sqrt((-10sec(θ))^2-100)

simplify

(- 10 sec (θ))^{2} - 100

10 tan (θ)

Solution steps

(- 10 sec (θ))^{2} - 100

(- 10 sec (θ))^{2} = 1 0^{2} sec^{2} (θ)

= 1 0^{2} sec^{2} (θ) - 100

Factor

1 0^{2} sec^{2} (θ) - 100 : 100 (sec^{2} (θ) - 1)

= 100 (sec^{2} (θ) - 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 100 sec^{2} (θ) - 1

100 = 10

= 10 sec^{2} (θ) - 1

Use the Pythagorean identity:

sec^{2} (x) = tan^{2} (x) + 1

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

= 10 tan^{2} (θ)

tan^{2} (θ) = tan (θ)

= 10 tan (θ)

sin (2 t) - sin (- 2 t)

2 sin (x - 3 0^{\circ}) + sin (x)

5 cos (+ 7 sin^{2} (- 2 cos (x)))

2 cos^{2} (x) - sin (- 1)

3 sin (π x - \frac{π}{5})

What is sqrt((-10sec(θ))^2-100) ?
The solution to sqrt((-10sec(θ))^2-100) is 10tan(θ)