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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= sec^{2} (α) + 1

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + sec ( x )}{csc ( x )} - tan (x) = sin (x)

2 sin (x) = \frac{4 cos ( x ) - 1}{tan ( x )}

cos (8 x) = cos^{2} (4 x) - sin^{2} (4 x)

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

\frac{cot ^{2} ( x )}{cos ( x )} = cot (x) \cdot csc (x)

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