What is expand tan^2(x)(csc(x)-1)^2 ?

The solution to expand tan^2(x)(csc(x)-1)^2 is tan^2(x)csc^2(x)-2tan^2(x)csc(x)+tan^2(x)

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expand tan^2(x)(csc(x)-1)^2

expand

tan^{2} (x) (csc (x) - 1)^{2}

tan^{2} (x) csc^{2} (x) - 2 tan^{2} (x) csc (x) + tan^{2} (x)

Solution steps

tan^{2} (x) (csc (x) - 1)^{2}

Expand

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

= tan^{2} (x) (csc^{2} (x) - 2 csc (x) + 1)

Apply the distributive law:

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

tan^{2} (x) (csc^{2} (x) - 2 csc (x) + 1) = tan^{2} (x) csc^{2} (x) + tan^{2} (x) (- 2 csc (x)) + tan^{2} (x) \cdot 1

= tan^{2} (x) csc^{2} (x) + tan^{2} (x) (- 2 csc (x)) + tan^{2} (x) \cdot 1

Simplify

tan^{2} (x) csc^{2} (x) + tan^{2} (x) (- 2 csc (x)) + tan^{2} (x) \cdot 1 : tan^{2} (x) csc^{2} (x) - 2 tan^{2} (x) csc (x) + tan^{2} (x)

= tan^{2} (x) csc^{2} (x) - 2 tan^{2} (x) csc (x) + tan^{2} (x)

(tan (x) + tan (y)) cos (x) cos (y)

- \frac{2}{( 1 - r ) ^{2}}

(x) \cdot (x - 14)

(cos (x))^{4}

\frac{1}{( x - n ) ( x - na ) ( x - n a ^{2} )}

What is expand tan^2(x)(csc(x)-1)^2 ?
The solution to expand tan^2(x)(csc(x)-1)^2 is tan^2(x)csc^2(x)-2tan^2(x)csc(x)+tan^2(x)