Is cos^4(x)+sin^4(x)=cos(2x) ?

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

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prove cos^4(x)+sin^4(x)=cos(2x)

prove

cos^{4} (x) + sin^{4} (x) = cos (2 x)

False

Solution steps

cos^{4} (x) + sin^{4} (x) = cos (2 x)

Show that the two sides are not equal

For

cos^{4} (x) + sin^{4} (x) = cos (2 x)

plug in

x = 1

cos^{4} (1) + sin^{4} (1) = 0.58658 \dots

cos^{4} (1) + sin^{4} (1)

Refine to a decimal form

= 0.58658 \dots

cos (2 \cdot 1) = - 0.41614 \dots

cos (2 \cdot 1)

Refine to a decimal form

= - 0.41614 \dots

The two sides are not equal

\Rightarrow False

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

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

sec (x) + tan (x) = \frac{1 + sin ( x )}{cos ( x )}

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

cos (x y) = cos ((y - 2) x) - 2 sin (x) sin ((y - 1) x)

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