What is the value of cos(pi/3)-2cos^2(pi/3) ?

The value of cos(pi/3)-2cos^2(pi/3) is 0

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cos(pi/3)-2cos^2(pi/3)

cos (\frac{π}{3}) - 2 cos^{2} (\frac{π}{3})

0

Solution steps

cos (\frac{π}{3}) - 2 cos^{2} (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

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

Simplify

\frac{1}{2} - 2 (\frac{1}{2})^{2} : 0

\frac{1}{2} - 2 (\frac{1}{2})^{2}

2 (\frac{1}{2})^{2} = \frac{1}{2}

2 (\frac{1}{2})^{2}

(\frac{1}{2})^{2} = \frac{1}{2 ^{2}}

(\frac{1}{2})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

Apply rule

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

= 2 \cdot \frac{1}{2 ^{2}}

Multiply fractions:

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

= \frac{1 \cdot 2}{2 ^{2}}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2}{2 ^{2}}

Cancel the common factor:

2

= \frac{1}{2}

= \frac{1}{2} - \frac{1}{2}

Add similar elements:

\frac{1}{2} - \frac{1}{2} = 0

= 0

= 0

cos (13 5^{\circ} - 3 0^{\circ})

2 (- 1) cos (2 (- 1)) - ((- 1) + 1)^{2}

5 sin^{4} (3) cos (3)

cos (2 9^{\circ}) \cdot 46.6 \cdot 2 \cdot \frac{22.5}{9.8}

cos (4 5^{\circ}) tan (3 0^{\circ})

What is the value of cos(pi/3)-2cos^2(pi/3) ?
The value of cos(pi/3)-2cos^2(pi/3) is 0