Is cos(4x)=1-8sin^2(x)cos(x) ?

The answer to whether cos(4x)=1-8sin^2(x)cos(x) is False

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prove cos(4x)=1-8sin^2(x)cos(x)

prove

cos (4 x) = 1 - 8 sin^{2} (x) cos (x)

False

Solution steps

cos (4 x) = 1 - 8 sin^{2} (x) cos (x)

Show that the two sides are not equal

For

cos (4 x) = 1 - 8 sin^{2} (x) cos (x)

plug in

x = 1

cos (4 \cdot 1) = - 0.65364 \dots

cos (4 \cdot 1)

Refine to a decimal form

= - 0.65364 \dots

1 - 8 sin^{2} (1) cos (1) = - 2.06058 \dots

1 - 8 sin^{2} (1) cos (1)

Refine to a decimal form

= - 2.06058 \dots

The two sides are not equal

\Rightarrow False

\frac{( 1 )}{( 2 )} (cot (θ) - tan (θ)) = cot (2 θ)

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

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

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

3 sec^{2} (x) - 4 = 0

Is cos(4x)=1-8sin^2(x)cos(x) ?
The answer to whether cos(4x)=1-8sin^2(x)cos(x) is False