What is sqrt((9*tan(θ))^2+81) ?

The solution to sqrt((9*tan(θ))^2+81) is 9sqrt(sec^2(θ))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify sqrt((9*tan(θ))^2+81)

simplify

(9 \cdot tan (θ))^{2} + 81

9 sec^{2} (θ)

Solution steps

(9 tan (θ))^{2} + 81

Apply exponent rule:

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

= 9^{2} tan^{2} (θ) + 81

9^{2} = 81

= 81 tan^{2} (θ) + 81

Factor

81 tan^{2} (θ) + 81 : 81 (tan^{2} (θ) + 1)

= 81 (tan^{2} (θ) + 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 81 tan^{2} (θ) + 1

81 = 9

= 9 tan^{2} (θ) + 1

Rewrite using trig identities

= 9 sec^{2} (θ)

sin (- x^{2})

sin (n \cdot π) - sin (- n \cdot π)

csc (9 0^{\circ} - x) sin (x)

sin (18 0^{\circ} + B)

3 cos (\frac{1}{2} t + π)

What is sqrt((9*tan(θ))^2+81) ?
The solution to sqrt((9*tan(θ))^2+81) is 9sqrt(sec^2(θ))