What is sqrt((asec(θ))^2-a^2) ?

The solution to sqrt((asec(θ))^2-a^2) is atan(θ)

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simplify sqrt((asec(θ))^2-a^2)

simplify

(a sec (θ))^{2} - a^{2}

a tan (θ)

Solution steps

(a sec (θ))^{2} - a^{2}

Apply exponent rule:

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

= a^{2} sec^{2} (θ) - a^{2}

Factor out common term

a^{2}

= a^{2} (sec^{2} (θ) - 1)

Apply radical rule:

assuming

a \geq 0, b \geq 0

= a^{2} sec^{2} (θ) - 1

Apply radical rule:

assuming

a \geq 0

a^{2} = a

= a sec^{2} (θ) - 1

Use the Pythagorean identity:

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

sec^{2} (x) - 1 = tan^{2} (x)

= a tan^{2} (θ)

tan^{2} (θ) = tan (θ)

= a tan (θ)

csc (0.5582 x + \frac{π}{2}) + 3.5

- sin (θ + 9 0^{\circ})

(6 sin (\frac{y}{4} + π) + 8.9)^{2}

2 sin (x + (\frac{π}{2}))

sin (- k x) k

What is sqrt((asec(θ))^2-a^2) ?
The solution to sqrt((asec(θ))^2-a^2) is atan(θ)