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

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

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

prove

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

True

Solution steps

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

Manipulating right side

tan (x) sin (x)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{cot ( x ) tan ( x )}{sin ( x )} = csc (x)

tan (6 a) sec (3 a) = 2 sin (3 a) sec (6 a)

(1 - sin^{2} (a)) (1 + tan^{2} (a)) = 1

sin^{2} (x) + sin^{2} (x) cot^{2} (x) = 1

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