Is 2cos(3((11pi)/(12)))=-sqrt(2) ?

The answer to whether 2cos(3((11pi)/(12)))=-sqrt(2) is True

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prove 2cos(3((11pi)/(12)))=-sqrt(2)

prove

2 cos (3 (\frac{11 π}{12})) = - 2

True

Solution steps

2 cos (3 \cdot \frac{11 π}{12}) = - 2

Manipulating left side

2 cos (3 \frac{11 π}{12})

Simplify

2 cos (3 \frac{11 π}{12}) : - 2

2 cos (3 \cdot \frac{11 π}{12})

Multiply

3 \cdot \frac{11 π}{12} : \frac{11 π}{4}

3 \cdot \frac{11 π}{12}

Multiply fractions:

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

= \frac{11 π 3}{12}

Multiply the numbers:

11 \cdot 3 = 33

= \frac{33 π}{12}

Cancel the common factor:

3

= \frac{11 π}{4}

= 2 cos (\frac{11 π}{4})

cos (\frac{11 π}{4}) = - \frac{2}{2}

cos (\frac{11 π}{4})

cos (\frac{11 π}{4}) = cos (\frac{3 π}{4})

cos (\frac{11 π}{4})

Rewrite

\frac{11 π}{4}

2 π + \frac{3 π}{4}

= cos (2 π + \frac{3 π}{4})

Apply the periodicity of

cos

cos (x + 2 π) = cos (x)

cos (2 π + \frac{3 π}{4}) = cos (\frac{3 π}{4})

= cos (\frac{3 π}{4})

= cos (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 π}{4})

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{2}{2}

= - \frac{2}{2}

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

Simplify

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

Remove parentheses:

(- a) = - a

= - 2 \cdot \frac{2}{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

= - 2

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) + sin (θ) cot^{2} (θ) = csc (θ)

\frac{( cos ( x ) sec ( x ) )}{tan ( x )} = cot (x)

+ sin (z + w) = sin (z) cos (w) + cos (z) sin (w)

(sin^{2} (x) + cos^{2} (x))^{5} = 1

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

Is 2cos(3((11pi)/(12)))=-sqrt(2) ?
The answer to whether 2cos(3((11pi)/(12)))=-sqrt(2) is True