What is sqrt((3)^2+(-3tan(t))^2) ?

The solution to sqrt((3)^2+(-3tan(t))^2) is 3sqrt(sec^2(t))

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simplify sqrt((3)^2+(-3tan(t))^2)

simplify

(3)^{2} + (- 3 tan (t))^{2}

3 sec^{2} (t)

Solution steps

3^{2} + (- 3 tan (t))^{2}

(- 3 tan (t))^{2} = 3^{2} tan^{2} (t)

= 3^{2} + 3^{2} tan^{2} (t)

Factor

3^{2} + 3^{2} tan^{2} (t) : 9 (1 + tan^{2} (t))

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

9 = 3

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

Rewrite using trig identities

= 3 sec^{2} (t)

cos (\frac{π}{2} - 2 x)

cos (- 2 nπ)

f (x) = cos (9 0^{\circ} + arccos (x))

\frac{sin ( π + x )}{cos ( 2 π + x )}

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

What is sqrt((3)^2+(-3tan(t))^2) ?
The solution to sqrt((3)^2+(-3tan(t))^2) is 3sqrt(sec^2(t))