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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

= sin (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

cot (θ) \cdot sec (θ) = csc (θ)

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

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

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

cos^{2} (A) tan^{2} (A) = sin^{2} (A)

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