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

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

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

simplify

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

sec (2 x)

Solution steps

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

Express with sin, cos

= \frac{cos ^{2} ( x ) + sin ^{2} ( x )}{cos ^{2} ( x ) - sin ^{2} ( x )}

Rewrite using trig identities

= sec (2 x)

\frac{sin ( x ) + cos ( x )}{sin ( x ) cos ( x )}

\frac{12 + 24 + 15 \cdot 7 - 2 ^{3}}{4 - 21}

(3 x + 5)^{2}

\frac{6}{5} \cdot 2

6 \cdot 64

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