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

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

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

prove

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

True

Solution steps

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

Manipulating right side

1 - tan^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

4 sin^{2} (x) = 3 - 4 sin (x)

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

cot (θ) = \frac{1 + cos ( 2 θ )}{sin ( 2 θ )}

cos (\frac{1}{sin ( b )}) \frac{sin ( b )}{cos ( b )} = 1

csc (x) + cot (x) = cot (\frac{x}{2})

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