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

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

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

prove

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

True

Solution steps

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

Manipulating left 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

cot^{2} (θ) - cos^{2} (θ) = cot^{2} (θ) cos^{2} (θ)

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

\frac{1 + cos ( θ )}{cos ( θ )} = sec (θ) + 1

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

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

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