What is sqrt(a^2-(asin(x))^2) ?

The solution to sqrt(a^2-(asin(x))^2) is asqrt(cos^2(x))

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simplify sqrt(a^2-(asin(x))^2)

simplify

a^{2} - (a sin (x))^{2}

a cos^{2} (x)

Solution steps

a^{2} - (a sin (x))^{2}

Apply exponent rule:

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

= a^{2} - a^{2} sin^{2} (x)

Factor out common term

a^{2}

= a^{2} (1 - sin^{2} (x))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= a^{2} - sin^{2} (x) + 1

Apply radical rule:

assuming

a \geq 0

a^{2} = a

= a - sin^{2} (x) + 1

Rewrite using trig identities

= cos^{2} (x) a

cos (arcsin (\frac{9}{x}))

tan (π - θ)

sin (arctan (\frac{x}{5}))

cos (arcsin (\frac{4}{x}))

sin (arctan (\frac{x}{k}))

What is sqrt(a^2-(asin(x))^2) ?
The solution to sqrt(a^2-(asin(x))^2) is asqrt(cos^2(x))