Is (1-tan^4(x))/(1-tan^2(x))=sec^2(x) ?

The answer to whether (1-tan^4(x))/(1-tan^2(x))=sec^2(x) is True

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prove (1-tan^4(x))/(1-tan^2(x))=sec^2(x)

prove

\frac{1 - tan ^{4} ( x )}{1 - tan ^{2} ( x )} = sec^{2} (x)

True

Solution steps

\frac{1 - tan ^{4} ( x )}{1 - tan ^{2} ( x )} = sec^{2} (x)

Manipulating left side

\frac{1 - tan ^{4} ( x )}{1 - tan ^{2} ( x )}

Simplify

\frac{1 - tan ^{4} ( x )}{1 - tan ^{2} ( x )} : tan^{2} (x) + 1

= 1 + tan^{2} (x)

Rewrite using trig identities

= sec^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ( x )}{1 + cos ( x )} = tan (\frac{x}{2})

cos (4 x) = 1 - 2 sin^{2} (2 x)

cos (π - x) + sin (\frac{π}{2} + x) = 0

cot^{2} (x) csc^{2} (x) - cot^{2} (x) = cot^{4} (x)

arcsin (x) = csc (x)

Is (1-tan^4(x))/(1-tan^2(x))=sec^2(x) ?
The answer to whether (1-tan^4(x))/(1-tan^2(x))=sec^2(x) is True