What is (1-sin^2(x))^{3/2} ?

The solution to (1-sin^2(x))^{3/2} is cos^3(x)

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simplify (1-sin^2(x))^{3/2}

simplify

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

cos^{3} (x)

Solution steps

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

Use the Pythagorean identity:

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

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

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

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

2 \cdot \frac{3}{2} = 3

= cos^{3} (x)

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

tan (2 x) cot (\frac{π}{5} - x)

cos (θ + π) - sin (π - θ)

36 - (6 sin (x))^{2}

tan (48 π + x)