What is expand sin^2(x)(cot(x)+1)^2 ?

The solution to expand sin^2(x)(cot(x)+1)^2 is sin^2(x)csc^2(x)+2sin^2(x)cot(x)

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expand sin^2(x)(cot(x)+1)^2

expand

sin^{2} (x) (cot (x) + 1)^{2}

sin^{2} (x) csc^{2} (x) + 2 sin^{2} (x) cot (x)

Solution steps

sin^{2} (x) (cot (x) + 1)^{2}

Expand

(cot (x) + 1)^{2} : cot^{2} (x) + 2 cot (x) + 1

= sin^{2} (x) (cot^{2} (x) + 2 cot (x) + 1)

Apply the distributive law:

m (a + b + c) = ma + mb + m c

sin^{2} (x) (cot^{2} (x) + 2 cot (x) + 1) = sin^{2} (x) cot^{2} (x) + sin^{2} (x) \cdot 2 cot (x) + sin^{2} (x) \cdot 1

= sin^{2} (x) cot^{2} (x) + sin^{2} (x) \cdot 2 cot (x) + sin^{2} (x) \cdot 1

Simplify

sin^{2} (x) cot^{2} (x) + sin^{2} (x) \cdot 2 cot (x) + sin^{2} (x) \cdot 1 : sin^{2} (x) (csc^{2} (x) + 2 cot (x))

= sin^{2} (x) (csc^{2} (x) + 2 cot (x))

Apply the distributive law:

a (b + c) = ab + a c

sin^{2} (x) (csc^{2} (x) + 2 cot (x)) = sin^{2} (x) csc^{2} (x) + sin^{2} (x) \cdot 2 cot (x)

= sin^{2} (x) csc^{2} (x) + sin^{2} (x) \cdot 2 cot (x)

= sin^{2} (x) csc^{2} (x) + 2 sin^{2} (x) cot (x)

\frac{1}{x ( x ^{2} + 5 )}

- (\frac{2 ( 2 s + 11 )}{( s ( s + 5 ) )})

- \frac{5 ( x + 4 )}{2 ( x + 3 )}

\frac{2 ( 256 2 - 18 3 )}{5} + 120

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

What is expand sin^2(x)(cot(x)+1)^2 ?
The solution to expand sin^2(x)(cot(x)+1)^2 is sin^2(x)csc^2(x)+2sin^2(x)cot(x)