What is (1-sin^2(θ))^{3/2} ?

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

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simplify (1-sin^2(θ))^{3/2}

simplify

(1 - sin^{2} (θ))^{\frac{3}{2}}

cos^{3} (θ)

Solution steps

(1 - sin^{2} (θ))^{\frac{3}{2}}

Use the Pythagorean identity:

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

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

= (cos^{2} (θ))^{\frac{3}{2}}

Apply exponent rule:

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

assuming

a \geq 0

= cos^{2 \cdot \frac{3}{2}} (θ)

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

= cos^{3} (θ)

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

sin (A rc sin (- 3))

sin (arccot (2 x - 4))

2^{2} + (2 tan (t))^{2}

cos (12 0^{\circ} - t)