What is sqrt(25+(5tan(x))^2) ?

The solution to sqrt(25+(5tan(x))^2) is 5sqrt(sec^2(x))

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simplify sqrt(25+(5tan(x))^2)

simplify

25 + (5 tan (x))^{2}

5 sec^{2} (x)

Solution steps

25 + (5 tan (x))^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 25 + 5^{2} tan^{2} (x)

Factor

25 + 5^{2} tan^{2} (x) : 25 (1 + tan^{2} (x))

= 25 (1 + tan^{2} (x))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 25 tan^{2} (x) + 1

25 = 5

= 5 tan^{2} (x) + 1

Rewrite using trig identities

= 5 sec^{2} (x)

cos (\frac{cos ( θ )}{sin ( θ )})

sin (9 0^{\circ} - \frac{a}{2})

cos (72 0^{\circ} - x)

cos (9 0^{\circ} - θ) + sin (θ)

cos (2 x - \frac{2 π}{3})

What is sqrt(25+(5tan(x))^2) ?
The solution to sqrt(25+(5tan(x))^2) is 5sqrt(sec^2(x))