What is (tan(x))/(1-tan^2(x)cot^2(x)-1) ?

The solution to (tan(x))/(1-tan^2(x)cot^2(x)-1) is -tan(x)

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simplify (tan(x))/(1-tan^2(x)cot^2(x)-1)

simplify

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

- tan (x)

Solution steps

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

Subtract the numbers:

1 - 1 = 0

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

tan^{2} (x) = tan (x) tan (x)

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

Cancel the common factor:

tan (x)

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

Simplify

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

= - tan (x)

\frac{1}{2} \frac{cos ( 7 x )}{3} + cos (x)

\frac{( 2 x ^{4} - 4 x ^{2} )}{( 4 x )}

b^{2} - 25 x^{2}

3 (x + y) - (x + y)^{2}

x^{8} + x^{10}

What is (tan(x))/(1-tan^2(x)cot^2(x)-1) ?
The solution to (tan(x))/(1-tan^2(x)cot^2(x)-1) is -tan(x)