What is sqrt(9+9tan^2(x)) ?

The solution to sqrt(9+9tan^2(x)) is 3sqrt(sec^2(x))

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simplify sqrt(9+9tan^2(x))

simplify

9 + 9 tan^{2} (x)

3 sec^{2} (x)

Solution steps

9 + 9 tan^{2} (x)

Factor

9 + 9 tan^{2} (x) : 9 (1 + tan^{2} (x))

= 9 (1 + tan^{2} (x))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 9 tan^{2} (x) + 1

9 = 3

= 3 tan^{2} (x) + 1

Rewrite using trig identities

= 3 sec^{2} (x)

sin (x) sin (- x)

tan (θ) + tan (\frac{π}{2} - θ)

sin (\frac{3 π}{2} + θ)

3 cos (\frac{1}{2} x + π) - 5

- cos (- A)

What is sqrt(9+9tan^2(x)) ?
The solution to sqrt(9+9tan^2(x)) is 3sqrt(sec^2(x))