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

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

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

simplify

9 tan^{2} (a) + 9

3 sec (a)

Solution steps

9 tan^{2} (a) + 9

Factor

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

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

9 = 3

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

Use the Pythagorean identity:

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

= 3 sec^{2} (a)

sec^{2} (a) = sec (a)

= 3 sec (a)

cos (arctan (\frac{x}{9}))

- 3 cos (\frac{1}{2} x - 2 π)

sin (arcsin (\frac{2 x + 1}{3}))

sin (\frac{- πn}{2})

tan (arcsin (x + 2))