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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{tan ( x ) - 1}{sec ( x )}

Express with sin, cos

= - cos (x) + sin (x)

= sin (x) - cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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)

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

sec (x) = arccos (x)

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