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

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

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

prove

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

True

Solution steps

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

Manipulating left side

1 - tan (x)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

sin (2 t + π) = sin (2 t) cos (π) + cos (2 t) sin (π)

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

cot^{2} (α) = cos^{2} (α) + (cot (α) \cdot cos (α))^{2}

\frac{1}{tan ( α )} \cdot \frac{1}{cos ( α )} = \frac{1}{sin ( α )}

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

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