What is the value of 2sin(30)cos(30)(1-2sin^2(30)) ?

The value of 2sin(30)cos(30)(1-2sin^2(30)) is (sqrt(3))/4

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2sin(30)cos(30)(1-2sin^2(30))

2 sin (3 0^{\circ}) cos (3 0^{\circ}) (1 - 2 sin^{2} (3 0^{\circ}))

\frac{3}{4}

Solution steps

2 sin (3 0^{\circ}) cos (3 0^{\circ}) (1 - 2 sin^{2} (3 0^{\circ}))

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

= 2 \cdot \frac{1}{2} \cdot \frac{3}{2} (1 - 2 (\frac{1}{2})^{2})

Simplify

2 \cdot \frac{1}{2} \cdot \frac{3}{2} (1 - 2 (\frac{1}{2})^{2}) : \frac{3}{4}

= \frac{3}{4}

arccos (\frac{1.5}{8})

2 sin (7 5^{\circ}) cos (1 5^{\circ})

25 cos (3 7^{\circ})

100 \cdot sin (2 0^{\circ})

arctan (\frac{2.6}{- 1.1})

What is the value of 2sin(30)cos(30)(1-2sin^2(30)) ?
The value of 2sin(30)cos(30)(1-2sin^2(30)) is (sqrt(3))/4