What is the value of cos(45)*2 ?

The value of cos(45)*2 is square root of 2

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cos(45)*2

cos (4 5^{\circ}) \cdot 2

2

Decimal Notation

1.41421 \dots

Solution steps

cos (4 5^{\circ}) \cdot 2

Use the following trivial identity:

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

cos (4 5^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

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

Simplify

\frac{2}{2} \cdot 2 : 2

\frac{2}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

2

= 2

= 2

sec (39 0^{\circ})

\frac{8 tan ( \frac{π}{8} )}{1 - tan ^{2} ( \frac{π}{8} )}

cos^{2} (8)

sin (arcsin (\frac{3}{5}) - arccos (- \frac{8}{17}))

cos (\frac{π}{2}) - \frac{π}{2} sin (\frac{π}{2})