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

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

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prove (1-tan^2(x))/(cot^2(x)-1)=cos^2(x)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{1 - tan ^{2} ( 1 )}{cot ^{2} ( 1 ) - 1} = 2.42551 \dots

\frac{1 - tan ^{2} ( 1 )}{cot ^{2} ( 1 ) - 1}

Refine to a decimal form

= 2.42551 \dots

cos^{2} (1) = 0.29192 \dots

cos^{2} (1)

Refine to a decimal form

= 0.29192 \dots

The two sides are not equal

\Rightarrow False

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