Is (2cot(x))/(1+cot^2(x))=cos(2x) ?

The answer to whether (2cot(x))/(1+cot^2(x))=cos(2x) is False

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prove (2cot(x))/(1+cot^2(x))=cos(2x)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{2 cot ( 1 )}{1 + cot ^{2} ( 1 )} = 0.90929 \dots

\frac{2 cot ( 1 )}{1 + cot ^{2} ( 1 )}

Refine to a decimal form

= 0.90929 \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

sin^{2} (x) cos^{2} (x) = \frac{1}{8} (1 - sin (4 x))

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

(sin (A) + cos (A))^{2} = 1 + 2 sin (A) cos (A)

\frac{cos ( b )}{sec ( b )} + \frac{sin ( b )}{csc ( b )} = csc^{2} (b) - cot^{2} (b)

2 cos^{2} (\frac{θ}{2}) - cos (θ) - 1 = 0

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