Is cot(2x)=(cot(2x)-1)/(2cot(x)) ?

The answer to whether cot(2x)=(cot(2x)-1)/(2cot(x)) is False

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prove cot(2x)=(cot(2x)-1)/(2cot(x))

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

cot (2 \cdot 1) = - 0.45765 \dots

cot (2 \cdot 1)

Refine to a decimal form

= - 0.45765 \dots

\frac{cot ( 2 \cdot 1 ) - 1}{2 cot ( 1 )} = - 1.13508 \dots

\frac{cot ( 2 \cdot 1 ) - 1}{2 cot ( 1 )}

Refine to a decimal form

= - 1.13508 \dots

The two sides are not equal

\Rightarrow False

tan^{2} (x) csc^{2} (x) - tan^{2} (x) = 1

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

tan^{2} (x) - (sec (x) + 1) (sec (x) - 1) = 0

csc (u) sin (u) - cos^{2} (u) = sin^{2} (u)

2 cos^{2} (u) - cos (2 u) = 1

Is cot(2x)=(cot(2x)-1)/(2cot(x)) ?
The answer to whether cot(2x)=(cot(2x)-1)/(2cot(x)) is False