What is sqrt(9-(3cos(x))^2) ?

The solution to sqrt(9-(3cos(x))^2) is 3sqrt(sin^2(x))

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simplify sqrt(9-(3cos(x))^2)

simplify

9 - (3 cos (x))^{2}

3 sin^{2} (x)

Solution steps

9 - (3 cos (x))^{2}

Apply exponent rule:

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

= 9 - 3^{2} cos^{2} (x)

Factor

9 - 3^{2} cos^{2} (x) : 9 (1 - cos^{2} (x))

= 9 (1 - cos^{2} (x))

Apply radical rule:

assuming

a \geq 0, b \geq 0

= 9 - cos^{2} (x) + 1

9 = 3

= 3 - cos^{2} (x) + 1

Rewrite using trig identities

= 3 sin^{2} (x)

sin (cos (- 1 (x)))

\frac{2}{1 + tan ^{2} ( x )}

sin (4 t + \frac{π}{3})

cos (2 t - π)

cos (\frac{3 π}{2} - θ)

What is sqrt(9-(3cos(x))^2) ?
The solution to sqrt(9-(3cos(x))^2) is 3sqrt(sin^2(x))