What is expand 1/(cos(x)(sec(x)-tan(x))) ?

The solution to expand 1/(cos(x)(sec(x)-tan(x))) is 1/(1-sin(x))

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expand 1/(cos(x)(sec(x)-tan(x)))

expand

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

\frac{1}{1 - sin ( x )}

Solution steps

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

Expand

cos (x) (sec (x) - tan (x)) : cos (x) sec (x) - cos (x) tan (x)

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

sec (x) cos (x) = 1

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

Simplify

1 - cos (x) tan (x) : - sin (x) + 1

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

\frac{4}{( x ^{2} + x ) ( x + 3 ) ( x ^{2} + 4 ) ( x + 2 ) ( x + 4 )}

- \frac{( 2 - x ) ^{2}}{4}

\frac{y u ^{2}}{u ∣ u ∣}

cos (0.2)

(3 x^{2} - 2 x y + 2) d x + (6 y^{2} - x^{2} + 3) d y

What is expand 1/(cos(x)(sec(x)-tan(x))) ?
The solution to expand 1/(cos(x)(sec(x)-tan(x))) is 1/(1-sin(x))