What is sqrt(25-(5sin(x))^2) ?

The solution to sqrt(25-(5sin(x))^2) is 5sqrt(cos^2(x))

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simplify sqrt(25-(5sin(x))^2)

simplify

25 - (5 sin (x))^{2}

5 cos^{2} (x)

Solution steps

25 - (5 sin (x))^{2}

Apply exponent rule:

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

= 25 - 5^{2} sin^{2} (x)

Factor

25 - 5^{2} sin^{2} (x) : 25 (1 - sin^{2} (x))

= 25 (1 - sin^{2} (x))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 25 - sin^{2} (x) + 1

25 = 5

= 5 - sin^{2} (x) + 1

Rewrite using trig identities

= 5 cos^{2} (x)

- \frac{sin ( a )}{sin ( - a )}

cos (x) cos (x + 18 0^{\circ})

2 sin (2 t - \frac{π}{2})

a r tan (- \frac{3}{2})

cos (nπ) + cos (π)

What is sqrt(25-(5sin(x))^2) ?
The solution to sqrt(25-(5sin(x))^2) is 5sqrt(cos^2(x))