What is the value of (sin^2(45)cos^2(45))^{3/2} ?

The value of (sin^2(45)cos^2(45))^{3/2} is 1/8

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(sin^2(45)cos^2(45))^{3/2}

(sin^{2} (4 5^{\circ}) cos^{2} (4 5^{\circ}))^{\frac{3}{2}}

\frac{1}{8}

Solution steps

(sin^{2} (4 5^{\circ}) cos^{2} (4 5^{\circ}))^{\frac{3}{2}}

Use the following trivial identity:

sin (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

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

Simplify

(\frac{2}{2})^{2} (\frac{2}{2})^{2}^{\frac{3}{2}} : \frac{1}{8}

= \frac{1}{8}

cot (\frac{- 11 π}{6})

arccos (\frac{3}{18})

\frac{cos ( 0.01 ) - 1}{0.01}

cos (\frac{5 π}{18}) cos (\frac{2 π}{9}) - sin (\frac{5 π}{18}) sin (\frac{2 π}{9})

arcsin (sin (- \frac{7 π}{6}))

What is the value of (sin^2(45)cos^2(45))^{3/2} ?
The value of (sin^2(45)cos^2(45))^{3/2} is 1/8