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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ( 2 x )}

Rewrite using trig identities

sec (2 x)

We showed that the two sides could take the same form

\Rightarrow True

1 - \frac{cos ^{2} ( a )}{1 + sin ( a )} = sin (a)

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

\frac{sin ( 3 x ) - sin ( 5 x )}{2 cos ( 4 x )} = - sin (x)

sec^{2} (x) - 1 = \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

tan (a) + cot (a) = 2 csc (2 a)

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