Is cos(4x)+4cos(2x)+3=8cos^2(x) ?

The answer to whether cos(4x)+4cos(2x)+3=8cos^2(x) is False

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prove cos(4x)+4cos(2x)+3=8cos^2(x)

prove

cos (4 x) + 4 cos (2 x) + 3 = 8 cos^{2} (x)

False

Solution steps

cos (4 x) + 4 cos (2 x) + 3 = 8 cos^{2} (x)

Show that the two sides are not equal

For

cos (4 x) + 4 cos (2 x) + 3 = 8 cos^{2} (x)

plug in

x = 1

cos (4 \cdot 1) + 4 cos (2 \cdot 1) + 3 = 0.68176 \dots

cos (4 \cdot 1) + 4 cos (2 \cdot 1) + 3

Refine to a decimal form

= 0.68176 \dots

8 cos^{2} (1) = 2.33541 \dots

8 cos^{2} (1)

Refine to a decimal form

= 2.33541 \dots

The two sides are not equal

\Rightarrow False

\frac{3 sin ^{2} ( 2 x )}{2} = \frac{3 cos ( 4 x )}{4}

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

cos (θ) = 3

1.5 sin (2 a) cos (2 a) = sin (3 a)

\frac{1}{1 - cot ( x )} = 1 - tan (x)

Is cos(4x)+4cos(2x)+3=8cos^2(x) ?
The answer to whether cos(4x)+4cos(2x)+3=8cos^2(x) is False