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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{1}{1 - cot ( 1 )} = 2.79401 \dots

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

Refine to a decimal form

= 2.79401 \dots

1 - tan (1) = - 0.55740 \dots

1 - tan (1)

Refine to a decimal form

= - 0.55740 \dots

The two sides are not equal

\Rightarrow False

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1 + (tan (a))^{2} = 1 + tan^{2} (a)

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

1 - sin (x) = cot (x)