What is sqrt(4-(2cos(θ))^2) ?

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

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simplify sqrt(4-(2cos(θ))^2)

simplify

4 - (2 cos (θ))^{2}

2 sin^{2} (θ)

Solution steps

4 - (2 cos (θ))^{2}

Apply exponent rule:

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

= 4 - 2^{2} cos^{2} (θ)

Factor

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

= 4 (1 - cos^{2} (θ))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 4 - cos^{2} (θ) + 1

4 = 2

= 2 - cos^{2} (θ) + 1

Rewrite using trig identities

= 2 sin^{2} (θ)

- cos (π + a)

cos (θ + 2 π)

2 cos^{3} (π x) + cos^{2} (π x) - 1

tan (x + π) cos (x - \frac{π}{2})

- 3 cos (3 x + π)

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