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

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

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

simplify

9 tan^{2} (x) + 9

3 sec^{2} (x)

Solution steps

9 tan^{2} (x) + 9

Factor

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

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

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)

cos (- 3 t)

sin (t^{2} - \frac{π}{2})

k^{2} - k^{2} sin^{2} (t)

cos (arcsin (ln (x)))

cos (arcsin (- cos (x)))

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