What is expand (cot(x)-1)(sqrt(3)cot(x)+1) ?

The solution to expand (cot(x)-1)(sqrt(3)cot(x)+1) is sqrt(3)cot^2(x)+cot(x)(1-sqrt(3))-1

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expand (cot(x)-1)(sqrt(3)cot(x)+1)

expand

(cot (x) - 1) (3 cot (x) + 1)

3 cot^{2} (x) + cot (x) (1 - 3) - 1

Solution steps

(cot (x) - 1) (3 cot (x) + 1)

Apply FOIL method

(cot (x) - 1) (3 cot (x) + 1) : 3 cot^{2} (x) + cot (x) (1 - 3) - 1

= 3 cot^{2} (x) + cot (x) (1 - 3) - 1

(sec^{2} (3 x^{2} + 6 x^{7} - 4)) \cdot (6 x + 42 x^{6})

\frac{( n + 1 ) ^{2}}{3 ( 3 n + 2 ) ( 3 n + 1 )}

\frac{( s + 3 )}{( s + 2 ) ( s + 5 ) ( s + 7 )}

\frac{1}{x ( 3 - x )}

\frac{200 ( s + 4 ) ^{2}}{s ^{2} ( 10 + s ) ( 20 + s )}

What is expand (cot(x)-1)(sqrt(3)cot(x)+1) ?
The solution to expand (cot(x)-1)(sqrt(3)cot(x)+1) is sqrt(3)cot^2(x)+cot(x)(1-sqrt(3))-1