What is (4-4sin^2(x))^{3/2} ?

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

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simplify (4-4sin^2(x))^{3/2}

simplify

(4 - 4 sin^{2} (x))^{\frac{3}{2}}

8 (cos^{2} (x))^{\frac{3}{2}}

Solution steps

(4 - 4 sin^{2} (x))^{\frac{3}{2}}

Factor

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

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

Apply exponent rule:

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

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

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

= 8 (- sin^{2} (x) + 1)^{\frac{3}{2}}

Rewrite using trig identities

= (cos^{2} (x))^{\frac{3}{2}} \cdot 8

a r csc (- 1)

tan (3 π + θ)

\frac{ln ( sin ( x ) )}{cos ( x )}

cos (\frac{π}{2} - θ) + cos (θ)

8.32 cos (400 t - 3.69)

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