What is sqrt(a^2+(atan(x))^2) ?

The solution to sqrt(a^2+(atan(x))^2) is asqrt(sec^2(x))

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simplify sqrt(a^2+(atan(x))^2)

simplify

a^{2} + (a tan (x))^{2}

a sec^{2} (x)

Solution steps

a^{2} + (a tan (x))^{2}

Apply exponent rule:

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

= a^{2} + a^{2} tan^{2} (x)

Factor out common term

a^{2}

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

Apply radical rule:

assuming

a \geq 0

a^{2} = a

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

Rewrite using trig identities

= sec^{2} (x) a

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What is sqrt(a^2+(atan(x))^2) ?
The solution to sqrt(a^2+(atan(x))^2) is asqrt(sec^2(x))