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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

tan (8 x) = \frac{2 tan ( x )}{1 - tan ^{2} ( x )}

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

\frac{1}{cot ^{2} ( x )} + sec (x) cos (x) = 1

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

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