What is (9-9sin^2(x))^{3/2} ?

The solution to (9-9sin^2(x))^{3/2} is 27cos^3(x)

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simplify (9-9sin^2(x))^{3/2}

simplify

(9 - 9 sin^{2} (x))^{\frac{3}{2}}

27 cos^{3} (x)

Solution steps

(9 - 9 sin^{2} (x))^{\frac{3}{2}}

Factor

9 - 9 sin^{2} (x) : 9 (1 - sin^{2} (x))

= (9 (1 - sin^{2} (x)))^{\frac{3}{2}}

Apply exponent rule:

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

= 9^{\frac{3}{2}} (- sin^{2} (x) + 1)^{\frac{3}{2}}

9^{\frac{3}{2}} = 27

= 27 (- sin^{2} (x) + 1)^{\frac{3}{2}}

Use the Pythagorean identity:

1 = cos^{2} (x) + sin^{2} (x)

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

= 27 (cos^{2} (x))^{\frac{3}{2}}

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

= 27 cos^{3} (x)

- \frac{2}{πn} cos (- πn)

\frac{sinh ( 4 x )}{cosh ( 2 x )} d x

cos (- a t)

sin (- y + π)

tan (\frac{π}{2} - A)