What is sqrt((10tan(θ))^2+100) ?

The solution to sqrt((10tan(θ))^2+100) is 10sqrt(sec^2(θ))

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simplify sqrt((10tan(θ))^2+100)

simplify

(10 tan (θ))^{2} + 100

10 sec^{2} (θ)

Solution steps

(10 tan (θ))^{2} + 100

Apply exponent rule:

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

= 1 0^{2} tan^{2} (θ) + 100

Factor

1 0^{2} tan^{2} (θ) + 100 : 100 (tan^{2} (θ) + 1)

= 100 (tan^{2} (θ) + 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 100 tan^{2} (θ) + 1

100 = 10

= 10 tan^{2} (θ) + 1

Rewrite using trig identities

= 10 sec^{2} (θ)

cos (θ - 27 0^{\circ})

cos (arcsin (cos (x)))

cos (arctan (3 m))

sec (arctan (- \frac{4}{3}) + πn)

tan (θ + 90 0^{\circ})

What is sqrt((10tan(θ))^2+100) ?
The solution to sqrt((10tan(θ))^2+100) is 10sqrt(sec^2(θ))