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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(1 - cos^{2} (x)) sec^{2} (x)

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

6 cos^{2} (x) - 6 sin^{2} (x) = 12 cos^{2} (x) - 6

sin (θ) cot (θ) sec (θ) = 1

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

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

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