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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

2 cos (2 \cdot 1) - 1 = - 1.83229 \dots

2 cos (2 \cdot 1) - 1

Refine to a decimal form

= - 1.83229 \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

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