Is sin(x)(sec(x)-csc(x))=tan(x)-1 ?

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

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prove sin(x)(sec(x)-csc(x))=tan(x)-1

prove

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

True

Solution steps

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

Manipulating left side

sin (x) (sec (x) - csc (x))

Express with sin, cos

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

Manipulating right side

tan (x) - 1

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

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

sec^{2} (x) csc^{2} (x) = csc^{2} (x) + sec^{2} (x)

cot (π - θ) = - cot (θ)

sec (x) + cos (x) = - sin^{2} (x) sec (x)

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

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