What is expand (1+sin(x)(1-sin(x)))/(cos(x)) ?

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

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expand (1+sin(x)(1-sin(x)))/(cos(x))

expand

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

cos (x) + tan (x)

Solution steps

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

Expand

1 + sin (x) (1 - sin (x)) : 1 + sin (x) - sin^{2} (x)

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

Simplify

1 + sin (x) - sin^{2} (x) : cos^{2} (x) + sin (x)

= \frac{cos ^{2} ( x ) + sin ( x )}{cos ( x )}

Rewrite using trig identities

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

Expand

(cos^{2} (x) + sin (x)) sec (x) : cos^{2} (x) sec (x) + sec (x) sin (x)

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

Rewrite using trig identities

= cos (x) + tan (x)

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

24 e^{(- 20 t)} + 20 (\frac{6}{5} - \frac{6}{5} e^{(- 20 t)})

\frac{d}{d t} ((x) (2 x + \frac{2 y}{3}))

\frac{k ( 3 k + 7 )}{2}

1 - e^{- 2 t} (2 - e^{- t})

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