Is cos^6(105)=((1+cos(210))/2)^3 ?

The answer to whether cos^6(105)=((1+cos(210))/2)^3 is True

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prove cos^6(105)=((1+cos(210))/2)^3

prove

cos^{6} (10 5^{\circ}) = (\frac{1 + cos ( 21 0 ^{\circ} )}{2})^{3}

True

Solution steps

cos^{6} (10 5^{\circ}) = (\frac{1 + cos ( 21 0 ^{\circ} )}{2})^{3}

Manipulating left side

cos^{6} (10 5^{\circ})

Expand

cos^{6} (10 5^{\circ}) : \frac{13}{32} - \frac{15 3}{64}

= \frac{13}{32} - \frac{15 3}{64}

Manipulating right side

(\frac{1 + cos ( 21 0 ^{\circ} )}{2})^{3}

Expand

(\frac{1 + cos ( 21 0 ^{\circ} )}{2})^{3} : \frac{13}{32} - \frac{15 3}{64}

= \frac{13}{32} - \frac{15 3}{64}

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (θ) = sin^{2} (θ) - 1

\frac{tan ( 2 θ ) + cot ( 2 θ )}{sec ( 2 θ )} = csc (2 θ)

\frac{sec ( θ )}{sec ( θ ) - 1} = \frac{1}{1 - cos ( θ )}

2 cos (θ) - \frac{cos ( 2 θ )}{cos ( θ )} = sec (θ)

cos (2 \cdot 30) = cos^{2} (3 0^{\circ}) - sin^{2} (3 0^{\circ})

Is cos^6(105)=((1+cos(210))/2)^3 ?
The answer to whether cos^6(105)=((1+cos(210))/2)^3 is True