Is (sin(x))/(cot(x)+csc(x))=1-cos(x) ?

The answer to whether (sin(x))/(cot(x)+csc(x))=1-cos(x) is True

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prove (sin(x))/(cot(x)+csc(x))=1-cos(x)

prove

\frac{sin ( x )}{cot ( x ) + csc ( x )} = 1 - cos (x)

True

Solution steps

\frac{sin ( x )}{cot ( x ) + csc ( x )} = 1 - cos (x)

Manipulating left side

\frac{sin ( x )}{cot ( x ) + csc ( x )}

Express with sin, cos

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

Manipulating right side

1 - cos (x)

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

tan (a) cos (a) = sin (a)

sin (x) (sec (x) + csc (x)) = tan (x) + 1

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

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

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

Is (sin(x))/(cot(x)+csc(x))=1-cos(x) ?
The answer to whether (sin(x))/(cot(x)+csc(x))=1-cos(x) is True