What is sqrt(4-(2sin(θ))^2) ?

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

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simplify sqrt(4-(2sin(θ))^2)

simplify

4 - (2 sin (θ))^{2}

2 cos^{2} (θ)

Solution steps

4 - (2 sin (θ))^{2}

Apply exponent rule:

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

= 4 - 2^{2} sin^{2} (θ)

Factor

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

= 4 (1 - sin^{2} (θ))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 4 - sin^{2} (θ) + 1

4 = 2

= 2 - sin^{2} (θ) + 1

Rewrite using trig identities

= 2 cos^{2} (θ)

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

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

sin (x + 3 0^{\circ})

tan (9 0^{\circ} - a)

sin (arccos (\frac{x}{4}))

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