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

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

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

prove

cos (4 x) - sin (4 x) = 1 - 2 sin (2 x)

False

Solution steps

cos (4 x) - sin (4 x) = 1 - 2 sin (2 x)

Show that the two sides are not equal

For

cos (4 x) - sin (4 x) = 1 - 2 sin (2 x)

plug in

x = 1

cos (4 \cdot 1) - sin (4 \cdot 1) = 0.10315 \dots

cos (4 \cdot 1) - sin (4 \cdot 1)

Refine to a decimal form

= 0.10315 \dots

1 - 2 sin (2 \cdot 1) = - 0.81859 \dots

1 - 2 sin (2 \cdot 1)

Refine to a decimal form

= - 0.81859 \dots

The two sides are not equal

\Rightarrow False

cos (x) tan^{3} (x) = sin (x) tan^{2} (x)

sin (x) = \frac{2}{2}

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

sin^{2} (0) = 4 (cos (- 0) - 1)

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

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