What is (4-4sin^2(θ))^{3/2} ?

The solution to (4-4sin^2(θ))^{3/2} is 8(cos^2(θ))^{3/2}

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simplify (4-4sin^2(θ))^{3/2}

simplify

(4 - 4 sin^{2} (θ))^{\frac{3}{2}}

8 (cos^{2} (θ))^{\frac{3}{2}}

Solution steps

(4 - 4 sin^{2} (θ))^{\frac{3}{2}}

Factor

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

= (4 (1 - sin^{2} (θ)))^{\frac{3}{2}}

Apply exponent rule:

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

= 4^{\frac{3}{2}} (- sin^{2} (θ) + 1)^{\frac{3}{2}}

4^{\frac{3}{2}} = 8

= 8 (- sin^{2} (θ) + 1)^{\frac{3}{2}}

Rewrite using trig identities

= (cos^{2} (θ))^{\frac{3}{2}} \cdot 8

cot (\frac{π}{2} - θ)

sin (θ + \frac{π}{6})

sin (x - \frac{π}{4}) + 1

tan (θ) sin (9 0^{\circ} - θ)

sin (13 5^{\circ} - x)

What is (4-4sin^2(θ))^{3/2} ?
The solution to (4-4sin^2(θ))^{3/2} is 8(cos^2(θ))^{3/2}