What is sqrt(a^2-(asin(θ))^2) ?

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

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simplify sqrt(a^2-(asin(θ))^2)

simplify

a^{2} - (a sin (θ))^{2}

a cos^{2} (θ)

Solution steps

a^{2} - (a sin (θ))^{2}

Apply exponent rule:

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

= a^{2} - a^{2} sin^{2} (θ)

Factor out common term

a^{2}

= a^{2} (1 - sin^{2} (θ))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= a^{2} - sin^{2} (θ) + 1

Apply radical rule:

assuming

a \geq 0

a^{2} = a

= a - sin^{2} (θ) + 1

Rewrite using trig identities

= cos^{2} (θ) a

sin (x - nπ)

sin (arccos (\frac{x}{7}))

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

5 sin (3 x - π)

cos (x + \frac{π}{2}) - cos (x)

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