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1 - tan2 A / 1 - cot2 A

June 5, 2026Mathematics

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Answer

-\tan^2 A

6 steps

Rewrite the expression by substituting $\cot^2 A$ with $\frac{1}{\tan^2 A}$ .
$\frac{1 - \tan^2 A}{1 - \cot^2 A} = \frac{1 - \tan^2 A}{1 - \frac{1}{\tan^2 A}}$
Simplify the denominator by finding a common denominator.
$1 - \frac{1}{\tan^2 A} = \frac{\tan^2 A}{\tan^2 A} - \frac{1}{\tan^2 A} = \frac{\tan^2 A - 1}{\tan^2 A}$
Substitute the simplified denominator back into the expression.
$\frac{1 - \tan^2 A}{\frac{\tan^2 A - 1}{\tan^2 A}}$
Multiply the numerator by the reciprocal of the denominator.
$(1 - \tan^2 A) \times \frac{\tan^2 A}{\tan^2 A - 1}$
Factor out $-1$ from the term $(1 - \tan^2 A)$ in the numerator.
$-( \tan^2 A - 1 ) \times \frac{\tan^2 A}{\tan^2 A - 1}$
Cancel out the common term $(\tan^2 A - 1)$ .
$-1 \times \tan^2 A = -\tan^2 A$
The simplified expression is:
$-\tan^2 A$

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