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

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

True

Solution steps

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

Manipulating left side

tan (x) - 1

Express with sin, cos

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

Use the basic trigonometric identity:

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

= (- cos (x) + sin (x)) sec (x)

= sec (x) (sin (x) - cos (x))

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

sin (x) - cos (x) = 1 - sin (2 x)

9 sec^{2} (x) - 5 tan^{2} (x) = 5 + 4 sec^{2} (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