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

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

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

simplify

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

2 cos^{2} (x)

Solution steps

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

Apply exponent rule:

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

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

Factor

4 - 2^{2} sin^{2} (x) : 4 (1 - sin^{2} (x))

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

4 = 2

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

Rewrite using trig identities

= 2 cos^{2} (x)

cot (\frac{π}{2} + x)

cos (arcsin (19 x))

tan (36 0^{\circ} + x)

cot (9 0^{\circ} - θ)

cos (θ + 9 0^{\circ})

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