What is sqrt(16-(4sin(x))^2) ?

The solution to sqrt(16-(4sin(x))^2) is 4sqrt(cos^2(x))

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simplify sqrt(16-(4sin(x))^2)

simplify

16 - (4 sin (x))^{2}

4 cos^{2} (x)

Solution steps

16 - (4 sin (x))^{2}

Apply exponent rule:

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

= 16 - 4^{2} sin^{2} (x)

4^{2} = 16

= 16 - 16 sin^{2} (x)

Factor

16 - 16 sin^{2} (x) : 16 (1 - sin^{2} (x))

= 16 (1 - sin^{2} (x))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 16 - sin^{2} (x) + 1

16 = 4

= 4 - sin^{2} (x) + 1

Rewrite using trig identities

= 4 cos^{2} (x)

sin (2 t - π)

cos (x - 36 0^{\circ})

tan (arcsin (5 x - 1))

sec (x) sin (\frac{π}{2} - x)

9 - (3 sin (θ))^{2}

What is sqrt(16-(4sin(x))^2) ?
The solution to sqrt(16-(4sin(x))^2) is 4sqrt(cos^2(x))